I really would not risk it Martin, especially of you are visiting the US where you can incur huge medical bills. Something, not connected in any way to your P and swallowing difficulties, could happen and then that would also not be covered as you had not advised them of your P and associated problems.
As for your camera theft scenario, I fully expect a claim would be denied as you have not made a full disclosure of relevant facts. The insurer could attribute the theft of your camera to you not being fully aware of risks in the area that you were travelling........ anything for them to have a get out clause.
Just a year ago I had an op to release a trapped nerve in my arm. It was sorted, full stop. Our annual travel insurance was due for its yearly medical screening AND, despite the fact that I had been in serious pain for many months prior to the op, and that the op had resolved this, they had the nerve, (sorry for the pun) to charge me an excess on our policy for the forthcoming year.
I was not confident enough to be sure that, if I accidentally fell over, or something else happened, that they would not attribute this to my operated on arm. They would also not cover other conditions that had previously not incurred an excess; thyroid and such, unless I paid the excess.