That top trim is a structural piece, so definitely don't try to fix it with a full tank.
It would be best to do it with an empty tank, but you are prob OK with the water level down to less than 10" or so. <The frame is mainly a brace against the tank bowing out. This is a function of the water depth. Shallower tanks less than a foot deep don't need this, so I am guessing that you would be OK with this water depth ... but I have never tried this myself ... I did it with tank empty.>
The actual procedure:
1. remove the old trim - it is siliconed in place. If it is not loose, you will prob have to break it to get some purchase to pry it off. Cut the silicone with a sharp knife at the vertical seams so you don't lift off the vertical seams n the process.
2. remove all old silicone under the trim - new silicone won't stick to old. I find a skew chisel the best tool, but you can use a razor. Again, be careful not to damage the vertical seams, or you will have to repair those.
3. Clean the glass with vinegar, let dry
4. Silicone the new frame in place, wait till it is cured - 24-48 hrs before refilling tank.