Hmm..
(As always, not legal advice, consult your lawyer, etc.)
This is what I'd do in that situation: I'd have her sign it today and send it out to you, then have him sign a duplicate copy when he comes back.
Doesn't sound like there's any intent to move, they've always been good tenants, and having the communication (emails) that they're going to stay as well as the extension signed by one is probably good enough for now, and not worth the whole "sign this digitally now!" thing, IMO.
But do whatever makes you feel comfortable/whatever your legal counsel advises you. Typically there's a clause in a lease that it automatically goes month-to-month at the end of the term, so you still have a valid, enforceable lease even without a signed extension. Those things would make it "good enough" for me, personally.