Yes. this 10 Gauge wire is thicker than needed. 12 gauge will probably work. But for a few pennies more (and 10 gauge wire has more outer sheathing protection), "up sizing" to thicker 10 gauge wire is worth it. Especially if you plan to keep your RV/TT for many years.
Also remember that with inertia brake controllers (like Prodigy Px models), one should be driving > 20 MPH to test the trailer brakes. Having trailer hub on jack / block and apply TV's brake peddle won't activate its internal inertia trigger. In other words, TT brake hub won't often activate.