I just did this - replaced the cottered spindle with a square taper spindle. Took the cups, bearings, and old spindle to the bike coop and looked through their box of old spindles. Cost $8.

Now, I did that because the bike had a French thread bottom bracket and a cartridge BB for that thread is $50 + shipping. If I had standard English threads and thus the option of a cheap standard cartridge BB, I'd do that instead.