Hi,
The Xavier should support mouse/keyboard wireless combo, In my case I use a similar combo with a single USB transceiver.
About your question
Yes, you can cross-compile the kernel, I haven’t tested docker images but they should work as well.
Some example steps to cross-compile the kernel can be check here: https://developer.ridgerun.com/wiki/index.php?title=Xavier/JetPack_4.1/Compiling_Code/Kernel
You will need to adjust the L4T version required for your desire JetPack version.
Regards,
Greivin F.