Can you play a shellac record on a vinyl player?

Yes, but you should replace the needle and/or cartridge first. The grooves on shellac records have a different size than vinyl records and if you use a vinyl needle on a shellac record, you can damage both the record and the needle.

Look on ebay for a "78rpm stylus" and find one that will fit in your cartridge. It'll generally cost around $20 (of course there are more expensive options like replacing the cartridge or higher quality styli).