TC-W2 or W3 is listed as suitable for engines listed in the service manual for 2002 (manual covers engines from 1996 till 2005 I think) 60 Jet through 125 HP engines. Only shelf life I can think of is additives settling out of it if it has a secured lid to keep environmental effects from contacting the contents. Sometimes I look in the bottom of (different types of) oil containers of different functions (engine, hydro, gear types) that I know have been sitting for a long time on retailers shelves, or mine, some having been partially used by me but lids were replaced and secured) for an extended period and have found few indications of that happening and only a very thin, spotty film when I do see such.
I had a clear plastic container with a lid on it of used diesel tractor engine oil that I sat up on a shelf once for some reason. I came back years later and the once black oil was honey colored and the bottom of the container had a thick layer of sludge. So there is an example of carbon not being homogenized in the manufacturing process like is the case with additives and over time settling out.
I bought a used 2002 rig a couple of years ago and it had a very dirty partially used WW TC-W3 gallon of engine oil stuffed under a seat. For the few bucks that it was worth, I didn't feel like I needed to use it. Haven't missed anything by my decision.