USB 3 Hard disk interferes with Wireless KB/M

This is a known potential issue with USB 3.0 and 2.4GHz wireless devices (which your wireless desktop set is very likely to be).

If you can connect the keyboard wireless adapter to the opposite site of the laptop from the external HDD you might get better results, or perhaps you can use a USB extension cable for the wireless adapter to reduce/eliminate the problem.

Those suggestions are from Using USB3.0 and 2.4Ghz USB wireless device on a notebook at the same time may experience radio frequency interference.. The phenomenon is acknowledged by Intel at USB 3.0* Radio Frequency Interference on 2.4 GHz Devices.

Shielded USB 3.0 cables are available, but the few reviews I looked at on Amazon seem to have mixed results.