I haven't looked at the USB stuff (yet), but here are som egenral ideas...

To sequentially select 1of N outputs with a pushbutton, I'd look at a setup with N flipflops configured to (hmmm, is it called a Johnson counter?) to move a "1" around the flipflops, looping back after it hits the last one. The pushbutton provides the "clock" signal that triggers the flipflops to move the "1" on to the next flipflop.

To connect the one USB port to 1 of 4 I'd look at bilateral switches (hopefully something with low enough "on" resistance is available) and the moving "1" enables one switch at a time.

Browsing a catalog I spotted the 4051/4052 8/2x4bit analog multiplexer/demultiplexer. That and a counter chip clocked by the pushbutton might do it (haven't read the the spec sheets, nor do I know the requirements of the USB bus)

/Michael