Hi, Daplew!
This topic is particularly close to my heart, because a year ago I was trying to imagine how tippy would a surf ski (Nelo Ocean Ski or Epic V14) be in relation to an old-school german K1 with a triangular shaped behind.
One thing is for sure, if You can paddle a K1 (especially a top boat like a Nelo Cinqo etc), then You will be infinitely stable in any surf ski. That is like a different kind of boat all together.
In the internet surf ski community, people tend to differentiate flat water and the ocean. That is definitely an important point to bring out, but not so much because of stability per se, but a necessary set of skills to paddle in marine conditions with waves, wind etc. You will always be super stable in a surf ski (because managing to paddle a tippy K1 with some bumps or small waves, is nowhere near paddling a surf ski in much larger waves - K1 is SUPER DIFFICULT), but if You don't have experience paddling through braking waves or surfing waves, You may be in danger by getting out on a top ski and not knowing what's gonna happen.
This summer, I lent my ski (Nelo Ocean Ski) to some young K1 paddlers to play on the beach with braking waves. All of them were super stable, but couldn't simply handle waves, because they didn't know what was possible on a ski. While all of them paddle top boats, which I will feel very unstable about, they were constantly falling out of the ski. Me, on the other hand, much much worse on a K1 on the flat, but was able to stay in the ski all of the time in waves.
So, to make a short story long.. don't even think You'll have problems with stability on a ski, but if planning to go out downwinding etc, please go with experienced people, check Your calf leash is on and strong, and be aware that the ocean or open sea is a serious place.. Paddle safe
P.S. I once too was planning to use the surf ski on flat water, but that changed very quickly.. so these posts talking about downwind are not a waste of time