I'm not sure about the procedure for submission of the sights for re-lamping that Trigicon uses, but can't you just remove the sights from the two guns and send the sights in? (If not, I personally would not have them re-lamped) As you said, it wouldn't be worth the risk to mail the slides to them. I agree completely.

Your other concerns about how to install tritium sights are, I believe, unfounded. I'm sure if you are confident on how to properly set up and use your sight pusher that you should be able to handle this without any problem. You should mark the sights as to which gun they came off of, so they can be re-installed in the same configuration....and on the same slide when they are returned.
Also, I've never understood why gun owners are so concerned about the sights being "exceptionally tight" during installation. If they are too tight, it's a very simple process to remove a small amount of material from the sight base in preparation for them to be installed into the dovetail. Proper fitting of the oversized bases is, or should be, part of the installation process, and insures the sight itself, and the slide, will not be damaged.

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Ret. LE, FA Instr, S&W Armorer