What I do for "mild" sticky tapes...like when they've been in poor environments, but the tape itself isn't the typical SSS kind....is to wrap some lint-free paper wipes (meant for critical cleaning applications) around a pencil.
I then hold the pencil/paper against the tape as it FW/RW applying mild pressure, but not disrupting the tape transportation.
It's a bit tricky at first, but once you get the hang of it, knowing where to apply the pencil/paper and how to hold the it so as not to have it go flying away on you, or causing the tape to jerk/jump and ending up with a mess...it works quite well.
With several winds of paper on the pencil, with each pass, I spin the pencil until I have no more clean paper, then I rip the off and continue. After 4-6 passes, the tape leaves less and less residue and becomes less and less sticky.
If cleaned up a lot of used reels this way, and once I've worked the tape a bunch of time....after that it runs smoother and smoother with each pass until there's no more stickiness and the heads/guides remain clean.
I got the idea from seeing a special rig on a 2" deck at a tape transfer house, where they had a couple of extra guides mounted, and on them was like a cotton cloth ribbon that they could clean/wind/clean/wind against the moving tape.
It was a much more slicker setup than my pencil approach...it was done to a spare deck that wasn't good for any REC/PB use...so it was just for cleaning tapes. I don't have a spare 2"....so I use the paper/pencil approach.
