It is very risky to move a glass tank with water in it, as they are designed to have support around the entire bottom, which you don't have while you are carrying it.
I'd put some tank water in a bucket, drain some clean water off the top and put the fish in the bucket with their familiar tank water. Drain the tank completely and scoop out at least 50% of the substrate, as that is very heavy and will stress the seams. Carry it over and set it back up again. As long as you keep everything wet during the process you can avoid a cycle, but you will stir up quite a bit of debris. If a lot of debris stays in the tank and is in the water column when you set it up again that could start a mini-cycle, so when you drain it try to syphon off as much debris as you can. Good luck!