How do I go about adding this guy:


onto this fella here:


Without damaging the guitar?
This is the first time I've dealt with acoustic archtops, so pardon my ignorance on the matter.

I'm hesitant about screwing into the guitar, so are there any alternatives?
Glues? Someway to keep it on through grip? Any suggestion would help really.
Not going to say "impossible"... But extremely difficult. That pickup is a dedicated Gretsch item intended for however Gretsch puts together their guitars. That mounting bracket fits onto some structure inside the instrument, likely the neck block.
A hole is cut in the top, and the wiring must be installed as well... You need the volume and tone controls at least, and a 1/4" cable jack.
You would have to do all this work through the hole cut for the pickup... A very difficult installation.
If you must amplify the guitar and don't wish to deal with a mic, then I submit the easiest installation would be an internally-mounted piezo pickup routed through an endpin jack and then run to a pre-amp to give you the tone controls you'd want.
Still not easy, you have to work through the F-holes.... But a good tech could manage.