I bought a mini dril to drill holes in some seashells.

I think you have to get a masonry or hardened drill bit. People who make jewelry use sharp awl like tools.

diamond tip drill bit?

You might look into diamond burrs to create your hole. They are used on glass and ceramic tile as well as other materials, and you might find a size that works best for your shells. https://smile.amazon.com/s/ref=nb_sb_noss_2?url=search-alias%3Daps&field-keywords=diamond+burrs

They come in different grits-- 300 very fine and 80 coarse-- and the come in different shapes that might fit your needs.

Then take a small plastic container and put a sponge on the bottom and fill the container with water so you can drill underwater. I drill glass and working underwater extends the life of the burrs.

Rather than trying to soften the shells, why not use a diamond burr to drill? Here's one set: https://www.amazon.com/Pwhite-Assorted-Diamond-Jewelry-Gemstones/dp/B074PPGL41/ref=sr_1_10?s=hi&ie=UTF8&qid=1507512008&sr=1-10&keywords=diamond+dental+burrs

Diamond burrs can be used on glass, stone, ceramics, and shells. I use them for glass and use them in water to extend the life of the burr. Use a shallow dish (I use Tupperware) and put a sponge at the bottom. Add water to cover the sponge and a bit beyond and drill away.

Do a bit of practice to get used to it.

There might be a bit in one of those assortments that will be that small.

The grits are easy: 300 grit is fine; 80 grit is coarse. A fine grit will take longer to get through the shell, but will produce a neater hole. Eighty grit will cut through the shell faster, and may leave a rougher hole. The higher the number, the finer the grit.