If I were you, I would bite the bullet and get the paddles. That sand is pretty loose. We had a few different paddle brands, and the only ones that didn't have any problem with leaks were the ITP Sand Stars. Something about the bead itself is a bit beefier, and matches the ITP aftermarket rims better. But I'm no tire guy.
We had an absolute blast, and I never even tried it without the paddles on the 700XX. But they still felt necessary, if that makes sense. My big Can Am did fine without paddles, but I think that's because the 26" tires roll easier in the sand.
You can go without the paddles. I used to go to little sahara all the time with my 250r's without paddle tires and had no problem. I did howerver end up buying a set of ITP V groove paddle tires to make it easier. The 700xx has plenty of torque just go check it out and then decide if you need paddles tires. Damn I wish i was closer to little sahara I would go with you. Great park, I have heard that Oklahoma has redone all the parks dont know about this one. The showers were a little ratty about 10 years ago.