I don't think you can delete from the total [Random] mode inherently, but then again I've never tried. I'll look closer tonight but I'm guessing you have already done so.
However, if you use a Squeezebox add on called "Multi-Library," you could do this. I use it to separate my classical from, well, everything else.
How is this different than just creating your own playlist? Well, with Multi-Library you don't have to keep adding songs to a playlist every time you add a new CD. It creates libraries based on including or excluding genres or any other possible tag you can think of. The libraries automatically update themselves every time your main Squeezebox library updates. No more remembering to add a new CD to multiple play lists or limiting your listening to a single genre at a time.
In your case,
You could therefore create a library that included all genres but excludes songs with the lowest "Rating" then simply demote songs you don't want. Again, much like a playlist, except you don't ever have to remember to add new songs to it when you rip them. They will automatically be there. This library could, of course, then be played randomly.
Multi-Library takes a bit of pondering over some detailed instructions to install but it's been managing my music seamlessly without any further effort since I first installed it. I have the following music libraries now that I never have to manually add tracks to, as long as I am consistent with my genres when I rip them.
Classical
Modern (essentially, this is a mix of absolutely every genre but excludes classical & Christmas)
Maritime (Maritime, Celtic, and local folk music)
Christmas (begrudgingly maintained for my wife.)
Anything else I actually enjoy being mixed in randomly.
All of the selections above use a lowest rating flag to automatically exclude a track I simply never want to hear. If I really need to hear it, I can still find it through the main Squeezebox library. I can't bring myself to delete music. I'm a music pack rat.
