Without knowing what you plan to do on this keyboard or where you will use it it is impossible for anyone to advise on whether you need low profile but unlesss you're planning to put it in a small bag I would suggest you don't. Same goes for wireless - you're going to have to charge it so if it's sitting on a desk anyway why not save money and just leave it 'plugged in'?
A quick read about the K1 shows the keycaps are not MX compatible so all the pretty ones you (may have) see(n) won't fit. I have no idea if you care about that. Another complaint is it has no feet so sits flat and again, maybe you like that?
More details please