3M self-fusing rubber tape. It fuses to itself and sticks to objects by being conformable to shapes plus being grippy because it’s rubbery. It won’t leave any gum on the item when removed.
See Tape 23 and Tape 70 on this pdf; https://multimedia.3m.com/mws/media/592238O/01-tapes-emd-2009-catalog.pdf?&fn=01_Tapes_v02.pdf
Alternatively, tool handle dip might work for some things. Platsi Dip is the most common brand.
Thanks for that detailed suggestion.