first let me say that I have sea kayaks and that I am not really looking for a sea kayak suggestion.
I also have a small sit on top kayak. Actually it is the very first kayak I have ever owned. Ocean Kayak - Hula. Short, wide. I have knee straps to get a little bit of edge control but they slip if I get hit by big waves from the side. I’ve had it now for about 10 years or less.
I take it to the beach when my sons go surfing. I have not tried to roll this sucker only because sometimes the waves are so strong that I don’t believe I could do it.
It is ok. I have a paddle leash. If I get dumped I just hold on to the paddle and the boat is not going anywhere. It works very well unless you count occasional extremity amputation.
I am slowly thinking about replacing this boat as it is showing beginning signs of oil canning. I don’t believe I want SINK surf boat but what would be a good choice for a surfing sit on top that does not use straps for knee bracing but that would allow me to roll if I wanted to try it?
rolling a Sit on Top
If you want to roll a sit on top, you’ll either need thigh straps, or a suicide strap. Without either you’ll just fall off when you capsize. When you say you want one without thigh straps, perhaps you mean that you’d prefer a suicide strap that goes over your lap? I think of that being most common on Wave Skis. They’re basically surf-boards you sit on.
you say suicide strap?
I might preffer to just fall off 
I do have straps but they are a pain as big watter moves them around and I sometimes just need to push them back in while I need to be bracing. I thought perhaps there were some surf kayaks with more ergonomical bracing alternatives.
some folks start off with an old WW boat
as I am doing, but many seem to gravitate to either a KAOS or a real surf kayak. A WS/Dagger Kaos or a Cobra Strike are popular sit on tops, folks seem to have a real good time with those. The people I know use thigh straps and one fellow has added straps he slips his feet under, in addition. I see the Kaos sold used in the $300 range regularly around where I am, of course everyone says they paid only $200 ;). If bought wisely, one could recover their investment if the choice didn’t fit your needs.
I went with an old WW boat because I wanted to use it for roll practice in a pool, with surf a secondary use.
more secure bracing
I think if you want more secure bracing you might consider sit-inside boats. SOTs are reassuring to people who are nervous about wet-exiting, but the downside is that they’re generally clumsy rollers. There are obvious advantages to developing a good roll in surf and rough conditions, so if that’s your goal, I’d go for a boat that will make that easier, and that’s probably a surf-specific SINK or whitewater boat (or the aforementioned suicide-machine).
hmm
I don't know. The rest of my boats are SINKS and I do try to practice rolling them in rougher water but the types of surfing waves I've been in (where I get toppled ass over teakettle and do a few underwater cartwheels before I fall out of the boat) I'm just too old to roll those things.
Plus the water is low in the surfzone and I don't want to wear a helmet. It is just easier to treat the yak as a surfboard, fall off and get back in.
Get better straps or go waveski
You can find straps that stay put. Part of the problem is your boat is a dog. The thigh strap attachment eyelets are not positioned correctly. You can put on some new paddeyes and get much better control of the boat. Personally I would just sell it and buy a used Cobra Strike or move up to a waveski.
Look at trying out a Cobra Strike, Rapido, Five-0 or Big Stick if you want to stick with SOTs. All but the Strike are now out of production.
A waveski with a seatbelt is the way to go if you want to roll. Reliably rolling a SOT after wipeouts just does not happen, you usually lose contact with the thigh straps. A strike at least has reliable foot straps to keep you in good control.
Try the www.sit-on-topkayaking forum for information from people who actually surf Sit On Tops instead of people who have opinions ...
For waveskis
Check out island waveski page, wavemasterusa and Infinity Surfboard webpages.
Also go to www.uswaveski.com for better info.
my advice . . .
Wear a helmet in the surf! Your head isn’t just there to make your neck look skinny. And a helmet isn’t just needed to keep your head off the bottom while you try to roll. Kayaks are heavy, and they’ll knock you silly when they get tossed by big surf. To me it sounds very dangerous to get maytagged with a 60 pound sit on top kayak, and no helmet. I know different folks have different risk profiles, but since you mention that you’re worried about hitting the bottom in a SINK, you may want to consider the risk of getting your onion split by your SOT during a wipeout.
agreed (in general)
in a wipeout, the kayak goes first. If you hang on to the paddle all you do you are just flying behind it like confetti.
good suggestions.
I will look those up.
kwikle
OP search archives for posts by kwikle (Keith Wikle).
He’s a very avid and skilled surf kayaker. He’ll tell you about Mega kayaks, the Valley models and others. He’s also an ACA instructor and will be at the Great Lakes Sea Kayak symposium coming up later this week.
gokayaknow.com is his website, you can see vids of him surfing Lake Michigan, and contact him thru there as well.