I bought a Sheaffer with the nib marked Fineline 304 with some printing on it from the refinery my Grandfather headed the maintenance department of most of his life. From what I can see and dig up, it's a cartridge pen. Yes?
If so, will it take modern Sheaffer caartridges? Is there a converter available for this pen?
It looks to be in great shape, but I think I'll have it looked over. Who's my best choice to do this?

It is indeed a cartridge pen. Any cartridge except the slim cartridge (no longer made) will fit the pen. The classic squeeze converter should fit, though there are some models that are cartridge only. If the standard converter won't fit because it's too wide, a Montiverdi mini converter may work.