I wouldn't either. A real problem with fuel system cleaners is they can cause fuel quality issues leading to detonation.
ONLY burn fresh clean high quality fuels in marine engines b/c the duty cycle is high unlike most any other application damage can occur quickly where it wouldn't happen otherwise, especially 2-strokes, anything older than a few months is suspect.
I feel so strongly about this, I avoid fuel stabilizer, I completely empty my boat tank for winter. If my fuel is beyond a few months old for whatever reason, I'll remove it and burn it in something else like an old lawnmower. If the fuel is really old and smells stale don't even do that, see if your local junkyard can recycle it.
Plan accordingly, use the fuel up last of season so it's easier to remove the remainder. Don't let those last few gallons sit in the tank over winter. If you cannot do this for winter storage in your case then add stabilizer and fill tank with fresh fuel to minimize air space in the tank. The problem with this is if the fuel sits there a couple years for whatever reason you have a complete tank full of questionable fuel that must be disposed of.