You ask for better, lighter.
You don't like the answers our experiences have given.
A pack towel is a pack towel, is a pack towel. Think outside the box.
My experience is.
Bought pack towel, too heavy
Light load towel. Gimmicy and not long lasting.
Handi wipes. Got hard to find these in the stores some times, but at this point I'd been bringing bandannas anyway.
Golf towel. Found it. OK but too heavy, melts
Bandanna, does not melt. Drys fast enough for me. Readily available. Easy to clean, find, replace.
What have you tried in your 40+ years? I've only got 3+ decades.
Edit: Serious questions added. How many nose rags do you take along? How do you deal with them once loaded? I got a thing about blowing my nose and don't unless it is a last choice option. Fortunately allergies usually bother my eyes.