It only costs you 85 cents? I pay three dollars. 
True enough, teflon tape doesn’t want to stay in place on the tube when you try to slide the head on… but it was really intended for use on threaded fittings.
I’ve had good luck with putting a wrap of black electrical tape around the top end of the tube first, and then heating it with a cigarette lighter just enough to make the adhesive get gummy.
Then peel off the electrical tape, and you’ll have a sticky surface that will hold onto the teflon tape good enough to get the whistle head back on the tube.
Slightly heating the teflon tape after you wrap it around the tube also seems to slightly shrink it, which produces a better hold.
Well, yeah… after I flashed the store clerk. 
Wanted you out of sight as quickly as possible, did she
I you want something a little stronger, use a glue gun that sewing people use, the glue melts and dries. Use the low temperature type.
It you need to adjust the whistle, a small lighter or candle flame will suffice.
Bloo, a teeny dab of cyanoacrylate gel (Super Glue gel) will hold the teflon in place long enough for you to get the wrap on. Just be sure you don’t glue yourself to the whistle, or let any leakage remain, or you might find the whistle very difficult to adjust, indeed!
Should you change your mind about the beeswax, just remember to hold the joint in your hand to warm it a bit before applying or adjusting. Here’s a link to application info: http://www.serpentmusic.com/beeswax1.html - I promise there are no subliminal messages there! 
serpent
I wish we could. Our local bees died out in some sort of disease here and it is hard to find real beeswax. It seems like the beeswax sells for lots more than honey, so it is hard to buy a jar with the comb still in it (my favorite way to get beeswax) nowadays. 