Would a new nut solve a string rattle issue? (not fret buzz)

[LJD]

The bass/wound strings on my HBII go wild when I dig in, and they rattle more than my other guitars. It's a very bright, lively instrument. The guitar shipped with 11 gauge strings (didn't rattle much with 11s), and I had my luthier set it up for 10s but we left the nut alone. Would a nut cut for 10's have any effect? Simpler question, what are the effects of not changing the nut when going down in string gauge size?

 

[CatStrangler]

are these rattles open strings or the first fret or two? If so I would say you might need a new nut if the current slots are cut too low for the 10's.