First of all, many manufacturers tend to voice their cabs to complement their amps - and vice versa. From what I've gathered, this is particularly the case with TC Electronic. How well it would work with your Hartke amp? I have no idea...
Secondly, no way is a single 1x12 ever going to substitute for a 4x10. A pair of 1x12s maybe. But only if they're extraordinary cabs...and/or if the 4x10 in question is mediocre at best. Take that as you will.
Thirdly - and therefore - it makes no sense whatsoever to expect to mate a single 1x12 cab with a 4x10, and actually expect the 1x12 to hold its own against the 4x10. Not gonna happen. What you get is "the worst of both worlds" scenario, with your total system performance limited by the relatively meager output of the 1x12, while the 4x10 languishes.
I suggest you think out your system requirements much more thoroughly...
FWIW, I did briefly own a Hartke HX112 a bit earlier this year. I expected to be impressed...and I wasn't. The thing couldn't handle much power at all, and just completely mushed out on the low end whenever pushed. Since I bought this thing used, on the aftermarket, it's entirely possible that it had been abused and beaten up before I ever got it. So take that with a pound of salt in consideration of a brand new unit. Just try before you buy...
MM