Sounds a lot more like a tubular polypropylene/film/wax or similar
capacitor than an electrolytic. Some of the better quality units
(safety ratings? Danger, Will Robinson, safety ratings! Especially in
a snubber on the AC line!) are in metal cans.

Tim.

So, how does one decisively determine the type?

There are no markings whatsoever other than the ones described. The plastic
insulation (shrink) covers all but the inner diameter of the ends. The leads
are connected to the (aluminum) end caps which are identical.
--
John English