@Battlefield – Mmm…I think it would be „I don't want to hang up“
for the telephone thing – „I don't want to stop talking to you on the
phone“. „Hang up on someone“ means to end the conversation abruptly, as in
anger. „He was so mad, he just hung up on me without saying
goodbye.“
If you don't want someone to end the conversation, you'd say „Don't hang up
on me“ or just „don't hang up“. But definitely not „don't hang me
up“ – that means don't poveset me
But as far as referring to a delay, „hang you up“ or „keep you
(waiting)“ or „hold you up“ are all correct, AFAIK. („hang you up“ is
new to me, but as I said earlier, it could be a regional difference)