In all the water sports situations I have been in I’ve never carried a mobile phone. Whilst I understand your situation and agree to some extent your reasons for it, I think you’re over thinking the basics.
The only safety gear I carry is a whistle, a damn good one.
I’ve been in situations that could be described as “extreme” but I know what to do and how to get out of the situation should I need too. I’ve never used the whistle yet, but I will continue to carry it just in case.
Back to your situation, I agree that trying to press anything with both cold/none working fingers or the lack of ability to the think straight is tricky. The bigger the better, whatever phone you choose.
I’d seek out MattOutandabout off here for his years as an instructor/outward bound expert, for should he be so inclined to give his expert advice on your choice decisions..
Just sayin..
I used to think the same, until we got caught out by a 35 kt (recorded) squall (this blew up from a F3-4, but in hindsight we now know northerlies at Stokes Bay do this sort of thing). We were very kindly escorted back in by a passing cruiser who also stood by whilst we waited out the worst of the weather upside down and dropped the (now holed) main. Thankfully no other damage that we noticed at the time*, so we made it back in, across an ebbing tide under jib. Coast guard had been called (by someone on shore), and whilst there was no formal report filed, it was firmly recommended to us that we carry some form of comms for reaching shore. I would feel a bit silly for ignoring their advice should we end up doing this again. I did find it mildly entertaining that the CG were sat watching events unfold in the comfort of their landrover, eating their sandwiches. Guess they figured we had it sussed.
The next step on from the self recovery would have been calling the club, politely asking for some assistance so as not to bother GAFIR/HMCG, so there is something here about making sure you get the right attention from the right people.
*We actually ended up losing the mast, which had cracked above top spreaders