There are loads of Catalytic Flueless gas fires available from
Fireplace Megastore They have all the information on each product for you to view and print for your gas fitter. I bought mine from here, now my nextdoor neighbour has one!!
To move it should be quite a simple job, although your right it will be messy for a week, but once moved it should be an easy job to install as the catalytic fires, just sort of hang on the wall then pug into the gas, it might be simpler to install an LPG version with a lpg gas bottle outside, if the new wall is an outside one!!