Safe lacquer to use on wood chess pieces?

Can anyone recommend a safe (non cancer-causing) lacquer to use on wooden chess pieces? A few years ago my wife brought back a wood chess set from the Philippines. The board and pieces are made from a very light, inexpensive type of wood. It's a type of chess set that is apparently made throughout the Philippines for everyday use by people who don't have much money (i.e., most people there). I enjoy using the set for study, but I'm thinking of painting the pieces with lacquer to give them a nice shine. As long as I can find some kind of safe lacquer that will not cause cancer.

And, possibly, I will put a weight on the bottom of each piece, if that can be done without ruining them.

Lacquer is a term that covers many things, and possibly not all of the things you are thinking about.  You aren't talking about traditional asian urushi lacquer which is highly allergenic in its un-cured form and difficult to work with.  There is a range of modern synthetic lacquers, some of which are water based.  The problem with the modern lacquers is the solvents, but you deal with that by applying them in a place with good ventilation and letting them sit for a while to fully cure.  There are other shiny finishes that you might look at, the question is how to get a synthetic finish to stick to whatever is on the pieces now, or how to sand the pieces so that you re coating clean bare wood.  

Carnauba wax is my recommendation, unless you really think the pieces need to be refinished. 

If it's like you said, and all they need is a good shine, carnauba wax ( the hard wax in bar form is easiest to use) and a buffing wheel will get you there. Shiny without being outrageous. 

If you really need to refinish them, and you want as natural a finish you can get, I think your best option is shellac. Basically bug spit. If you buy flakes, you don't have to worry about the aforementioned solvents, but the process is a bit involved. 

Raw flaxseed oil (just oil and no solvents added...can buy at the grocery store) is one of my favorites, but it takes forever to dry properly, and you won't get a high gloss shine.

Thanks, everyone, for the suggestions. 

The pieces are made of a very light, cheap wood. They are probably not worth refinishing. But I want to continue using this set, because my beloved wife brought it all the way from the Philippines.

Maybe carnauba wax would be a good solution. I assume it does not contain anything toxic. If you apply it to something, does it dry? Will it rub off on your fingers when you move the pieces? 

How much work is involved with shellac? 

Flaxseed is out. My wife is allergic to flax.

Carnauba is probably a good choice, its a hard wax (harder and shinier than beeswax) and isn't as far as I know toxic.  If your wife is sensitive to chemicals, all wax finishes will have some amount of a solvent in them to make them more easily spreadable, but the solvents evaporate fairly quickly once applied.  Waxes will wear off with a lot of use, but a wax finish can be reapplied easily.  

Shellac is not at all difficult, will stick to pretty much anything and is used in coating pills and things, so its not toxic at all, but it is so quick drying that it has its own set of problems in application.  Stick to the wax idea, you can buy pure carnauba in auto accessory stores (you do have to read the labels to find the pure one).

Another option to wax and shellac would be to use wipe-on polyurethane. That's what I used to refinish my pieces from House of Staunton when the original finish on those came off in my fingers.  (Ten months later I still haven't heard from them...)

I wouldn't recommend this for valuable, antique pieces as the finish is probably quite permanent and might be seen as devaluing them, but in your case I think it would be ideal. And once it's dried there is no chance of toxicity.

https://goneill.co.nz/chess-pieces.php

Here they are. A very simple set, made from light, inexpensive wood. 

Personally, I would coat them with flaxseed oil to give them a little natural color, wipe it all off after it gets a chance to soak, leave it alone for 2-3 weeks in a well circulated area, then go at it with the carnauba wax. 

Wipe on poly is great, but there are still a ton of water based solvents, and I only use it for finishing dining tables or other things that will need a hardier finish. 

Flaxseed in a no-no in our house. My wife is allergic to flax. 

Due to sensitivities to some finishes, you could consider simply burnishing the pieces with a polishing wheel and a spot of carnauba wax(as suggested). Just remember your PPE and how delicate the pieces may be. My $0.02 worth.

May I ask what is PPE?

After doing some research, I'm leaning toward either carnauba wax or shellac. I'm sure my nearby hardware store has shellac in spray form.  Thanks for all the suggestions, everyone!

From the picture, the surface of the pieces looks very rough, adding a shiny finish will make the roughness more obvious.  Just something to think about.  

My apology.. Personal Protective Equipment. My suggestion to use a polishing wheel wouldn’t be complete without a reminder to wear safety glasses etc. the wheel can really throw some fibers off while one is burnishing/polishing. I tend to wear a face shield over my glasses as well as my respirator/mask. Breathing in the small air borne fibers is something to avoid as well. All safely accomplished with the right precautions and well… PPE. Have fun with it!

Duh! Sorry, My brain was in chess mode, not pandemic mode. We have a niece who is an ICU nurse in California, and over the past year and a half we have had many sad conversations about what she is going through every day, trying to save lives. She once sent me a photo of her in full PPE at work. It made me cry.

Yes, I'm sure you are correct. But they will still look better than they do now, right?

I'm also thinking of "weighting" them by attaching a washer to the base of each piece, if I can find a glue that is non-toxic. 

I would suggest using high gloss Tung Oil.

I wound up buying a small can of shellac today at a nearby hardware store. We will see how that works.