Well, a #10 frog angle is arctan(1/10) = 5.7 degrees, so assuming there's no additional curve built into the switch you'll need a 5.7 degree crossover.
It looks like the shallowest crossing Atlas offers is 11.25 degrees, roughly twice what you need (and just about correct for a #5 switch). Honestly, I don't know if a 5.7-degree crossing would be viable without movable points--the odds of a wheel picking a point on such a shallow crossing would be pretty high.
In the situation you're describing, you might actually get smoother trackwork overall by dropping down to the #5 switches. After all, you'll have a fair length of tangent track between the turnouts, so the S-curve shouldn't be an issue.
(edit--stoopid typo)
