Hi,
There is no way to tell Live Mesh to use a different browser to your Internet default (Firefox).
Since Silverlight is fully supported on Firefox though, the only portion of the Live Desktop that you cannot access is the drag + drop (which only works one way, desktop -> browser, even in IE) and the Remote Desktop from within the browser (which I don't know why you'd want to do if you have the client installed).
Worst case, if you ever do need one of the above bits of functionality then you just open IE specifically and jump on mesh.com - you still need login regardless.
If you believe that this is a feature that should be added to Live Mesh then add it to the
Suggestions Sticky!
Cheers,
Oren