In theory, any of the Intel Compute Sticks could handle this, even the original STCK1A32WFC with its lowly Bay Trail Atom Z3735F processor. Handling it with ease? I would want to at least step up to at least the STK1AW32SC, which has the better-performing (both compute and graphics) Cherry Trail Atom x5-Z8300 processor. Understand that you will be using wireless communications regardless of which Stick you choose (though adding Ethernet support via USB is cheap enough).
Hope this helps,