Your basic generic cable tie is not air-safe. It gets brittle. This is ok for a lot of uses: either the cable tie is temporary, or it holds a fixed position. But it is not optimal for unused cable ties. Use sealed plastic bags. The plastic bags don’t need to be oven-bags: you’re only protecting cable-ties, not photographs.
That works, but if you need the stronger hold of duck tape, you can get no-residue duck tape. It’s very strong but doesn’t leave a mess when removed. Just costs a little more.
I have had cable ties that got old enough to get brittle. All of the current smaller ties had been in plastic bags and containers up until now, and the larger ones take a lot longer to become brittle. My concern now is convenience, open the drawer and easily find and remove cable tie(s) of the proper size. I have far more ties than I will need in normal circumstances and if they turn brittle I’ll get new ones.
Tape though, is a different subject. It has specific uses, and temporary bundling is not one of them. Masking tape shouldn’t leave a sticky residue. Any other kind of tape that doesn’t leave a sticky residue is called a strip of paper or plastic used like weak string.