Jim,
If your soldering iron isn't 'heavy' enough you can always
use a few bolts to attach the radials.
Another options besides the walls and desk top is the
ceiling,
hang the antenna from a hook. Or, if you're feeling
adventurous,
draw the antenna on a large sheet of paper with a graphite/lead
pencil, tape it where ever you want. Or use 'burglar alarm'
tape
on a window.
As Ian said, the 'best' option is to put the antenna
outside...
'Doc