Nope. Trump won't do that. Trump has demonstrated great patience as CiC and will continue to do so.
What Trump will do first is go back to China and the UN and demand action on NK. He will exhaust all possible options with China and the UN first before taking any direct military action. Trump is smart and wants to get China to take care of NK and avoid war if possible ... because Trump does have other fish to fry.
Nuking any US territory will force the US to nuke NOKO. Testing an open air weapon will fry someones’ electronics ... (things have changed since the West did open air testing) ... and force DJT to either do nothing but talk and appear weak (inviting a directed strike on the US by NOKO) or strong and wipe NOKO off the map. There is, at that point, no Third Way.
DJT either takes NOKO out or he and we get fried. Jabbering and pieces of paper are no threat to Kim. He will proceed as he plans: first the US, then SOKO and Japan. Perhaps these are his plans, or perhaps he is just fulfilling Xi’s plans.