Meshmy only issue is my 4th finger isn't long enough to cover all six strings and using a larger slide might be clumsy.......may have to use the 3rd (which will limit playing chords and such....).....trial and error it is.
You might well find you can cover six strings with a 4th finger slide, the slide kind of extends your finger and using one doesn't need much pressure at all - you don't press the strings down behind the fret to the fingerboard but let the slide float a little over the top of the frets or only just contact them. For good intonation the slide has to be over the centre of the fret, not behind it where you'd normally fret a note.
Too much pressure with a slide can cause more rapid than usual fret wear as well.
I've pretty small hands, use a long slide (Dunlop 222 size) and play 4,5 and 6 string chords at times without problems. As for damping, like everything about slide playing I doubt any two people do it exactly the same. I tend to damp mostly up at the bridge end with my right hand, but I usually play with fingers, not a pick.
Slide can feel very clumsy and out of control when you first try it, especially as every string the slide contacts wants to join in, sustain can be almost endless and open tunings are very resonant. So if playing electric, using a pretty clean amp setting might make things a bit easier to start with.