The random length wire should work okay for you,
and getting a ground isn't that hard at all! Go by
the garden ceter of Wal Marts, pick up a bag of
potting soil. Set the bag under your table where the
radio is and stick the end of a wire comming from the
ground terminal on your radio into the bag. Works
fine till all the moisture in the bag disapears, then
just wet the bag...
'Doc