It will handle most knives with no problem, on recurves for example the edges of the stone will work the recurve. As long as the curve allows the stone to make some contact. You have to be careful... this is a prime area where you use light pressure and "let the stone do the work". If you push down, the stone can cut into the side of the edge.
I believe you can also purchase the stones in 1/2 in. width, if it's a really tight curve or area you're trying to work.
You might want to contact edgepro directly and see if he's dealt specifically with the knives you're asking about.