I purchased an IC-705 to use for digital mode QRP operation. Quickly found out that my IC-705 is very sensitive to RFI coming in on the USB port, and did the same thing yours does.
I was able to decrease the issue somewhat by wrapping the USB cable to the IC-705 around some 240-43 ferrite donuts. More wraps is better and I have 10 wraps on mine.
The RFI was decreased some more by doing the same on the antenna output of the radio. Another 10 wraps. This doesn't totally eliminate the RFI, but it allows the radio to operate in digital mode fairly reliably.
If you do a Google search you'll find this is a common problem with the IC-705.