Do we think that contacting the swing vote senators, even if we are not in their state, might be a good plan right now?

Caveat: I am not an expert, but I've heard that as a rule, no; they will automatically ignore anything not from their potential voters.

Indivisible have a very good piece here:

https://www.indivisible.org/resource/not-call-members-arent/

and one does not have to live in their state to promise to fund their opponent next time around if they vote for this asshole.

You've seen the "either Collins votes no or we fund her future opponent" CrowdPAC, right?

https://www.crowdpac.com/campaigns/387413/either-sen-collins-votes-no-on-kavanaugh-or-we-fund-her-future-opponent

And I see there's now a Murkowski fund:

https://www.crowdpac.com/campaigns/388218/senator-murkowski-should-reject-kavanaugh

Pledges would be a very direct way to send that message, and I'm sure they'll notice!