I have this kind of super glue (cyanoacrylate), which the packaging implies it can be used either underwater or out of water, but that out of water would allow it to cure more thoroughly (it also says on the back about 20-60 sec is enough time for it to cure). Anything that's 100% silicone is also good to use, but that might definitely need to dry cure, I'm not sure. I actually haven't used it on anything since getting it (ended up tying my anubias with fishing line), so I can't be sure on the best methods, but YouTube videos all make it look easy enough.
As far as I can tell, that Aqueon kind is copper-free, and my snails, both big mystery and baby-thru-adult bladder, have been totally fine, so I imagine it would probably be fine for frogs. I actually saw yr cross-post in r/Aquariums and accidentally clicked thru to this main post, lol.
I bought this kind, but I think most cyanoacrylate adhesives will work, just let it dry/cure outside of the water.
Like this right?
https://www.amazon.com/RA-AquaTech-Aquarium-aquascaping-Instant/dp/B08H4XPCD2/
Never had to yet.