I'm not familiar with the Kensington product but I know that 10.4 changed some keyboard management. I'd been using an ADB-to-USB adapter under Panther to keep a much loved Apple M3501 ADB board in service. When I upgraded to Tiger, the adaptor caused many strange USB problem. I take it Kensington says you need 10.4?
As far as upgrading, assuming your current system and boot drive has no significant problems, the "Archive and Install" option offered by OSX will preserve your existing data and even most user settings and passwords. 384MB RAM is, IMHO, just a tad light for Tiger. More is better, but I tend to consider 512MB to be minimum for a happy Tiger experience.
The other option is to pick up a used older Apple USBkeyboard that's ± contemporary with the Cube. That would be much cheaper that finding a retail copy of Tiger (some places are now asking up to US$250 for legit disk sets) and a stick of RAM.