I'm not a pro, either, but I think that is a drum trap...and if it is, you'd never get a snake through it; it is also no longer approved, so replacing it with a new P-trap is a good idea. It doesn't look like it is vented, either, so to do it right will take more than just replacing that old trap with a new one. But, if you cut it off, you could use no-hub connectors and PVC to install a new trap in place. WIthout a vent, you risk siphoning the trap, which will open the drain to the sewer and any resulting smells, gasses, etc. If you local authorities allow AAV (air-admittance valves), you may be able to run that up behind the tub wall above the top of the tub (above the flood rim by at least 6"). But, since they can fail, they must be accessable for eventual replacement (normally takes many years, but still).