Late to the dance, but a few suggestions:
roof lenses (vs. Porro) - less spread, fewer moving parts, fold down smaller. Porros are more comfortable for some and some find them "brighter". They are the lens of choice for birdwatchers but we are up to something different.
Interpupillary range, which varies by model. So it's always better to try binocs on in the store as we all have a different distance between eye pupils that's best for our faces.
BaK7 lenses -these are the new standard. BaK6 are outdated. If you go BaK6 you should get them at a much discounted price.
magnification - 6x or 7x. Easier to see when water is bouncing.
The sailor's choice is overwhelmingly 7x but they are on a much more stable vessel compared to a kayak.
Close focus is not as important.
wide field of vision - if you use to scan coastline or to look for other vessels on the water. Less wide if for birdwatching.
Exit eye pupil 5 or lower. If your eyes are older they don't need as much light as a younger person's. A lot of marine binocs that are 7x50 (or with an exit eye of 7.7) provide more light than an older person's eyes can effectively utilize. Of course, if a kayaker is young and/or has 20/20 they can go w. a higher exit pupil spec.
nitrogen purged lenses & Orings - fogproofing.
Waterproofing - yes
Fully multicoated lens are the highest standard. Multicoated lenses follow. You don't need FMC lenses on the water.
eyecups if you wear prescription eyeglasses or just generic
sunglasses. Fold up or twistup are fine.
small is better - 12 oz or lower, ~4x3 inches max.
Floatation strap - don't ask '-)
I wound up finding some discontinued LL Bean 6x18s on eBay for under $10. They are 8 oz, 3.5 x 2.5" folded & will fit in a PFD pocket.
I also have some Leupold 6x30 porro prisms ( Yosemite series) but they weigh more & are much better for land use. very fun for critter watching. I like the little Beans, they are simple and do the basic job.
Nikon also has a small foldable set of binocs that will set you back ~$100 at REI. Other highly regarded brands that offer small, waterproof binocs are Vortex, Brunton and a slew of very expensive European makes. Unfortunately it is hard to find the 6x magnifiers and some Vortex and Brunton models in 6x can only be found discontinued. There also was a series developed for the Audubon Society (since discontinued) that is much coveted for their compact size and performance which offers 6x and 7x magnification.
Last thought is that some have tried and liked a monopod. Many of the same desirable features, one cylinder, smaller still.Vortex and Brunton make them, probably others.