Build a horn antenna for 10.525 GHz
I don't think this will work anywhere near as well as you expect it to. 

As you already found out, no waveguide (can) exist that supports single-mode propagation at your frequency requirements and dimensions. Even the WR-112 (which in theory only goes to 10 GHz) is only 28 mm on the long side. 

So lets say you use 4 waveguides, even then, I doubt you will gain anything with a horn. I suspect that the losses you will suffer because your entire system is not designed for a horn in the first place will result in your horns doing more harm than good. Keep in mind that this seems to already use a patch-antenna array, which means that it will already have a bit of directivity. 

I suspect if you want to do with with a horn antenna, you should start with a transmissionline to waveguide transition.