I don't think pasting a blockchain explorer link is overkill at all. When you send a screenshot, it's obviously an image, and it's not easy for the receiver to copy the hash out and paste it elsewhere so that they can validate it themselves.
It's like when someone emails a screenshot of a parcel tracking number -- I always curse them. I can either run it through OCR to get a copyable number, and OCR is likely to screw up a digit or two, or I can rekey the whole thing. I don't know which is worse, but they both suck.
Hell, you'd be better off emailing the hash as copyable text.
My 2 cents, anyway.