Could do with swapping headsets around frames – too tight to buy another one at the moment. Going back to HT from FS for winter & then back again in the spring. Frames are 2nd hand so they’ve had at least two headsets inserted already (original owner + one HT->FS move by me).

Removal of headset is via a pukka headset removal tool & reinsertion using a pukka headset press (if any of that makes a difference).

Does repetitive headset removal/insertion stress the headtube & should therefore be kept to a minimum?

or am I worrying about nothing…

Nope, do it with the proper kit and you’re fine – more likely to damage the cups than the frame.