Running this cartridge thru my modified Powley Computer (sort of a simplified QuickLoad), using a 25 grain bullet, a conservative 80% load density, and a few other assumptions, suggests a load of 30 grains of 4350 for 3,940 fps from a 22” barrel.
Flipping thru Wildcat Cartridges Volume II by Wolf Publishing there is there is an article, an old reprint from Handloader Magazine, titled “Those Amazing .17 Calibers” by none other than P.O. Ackley. He states 29 grains of 4350 for 3600 fps, and 33.5 grains of 4350 for 4,444 fps, from a 22” barrel.
He also tried 3031. 24 grains gave 3774 fps, 26 grains gave 4050 fps, and 28 grains gave 4275.
Were I to experiment with a .17-250 wildcat I would stick to moderately slow powders, in the speed range of N150, RL17, and 4350.