I would suggest that it is a job that a confident DIYer could undertake, I would certainly take it on myself.
You could protect the surrounding area with masking tape, to keep the paintwork protected, then gently warm the plate whilst slowing praising it off whith a flat scraper or blade.
A flexible putty/filler knife from B&Q or likewise would be ideal, it has a super thin but strong flexible blade, and would only cost a couple of pounds.
The masking tape would also protect the paint from the scraper/blade, or what ever you use.
Once the plate has started to come up it will probably lift easily, the trick is to start off gently on one edge/corner.
Once it's up, clean off any left over adhesive with something like WD40.
I would imagine the new plate will have a peel off double side adhesive tape already on the back ready to just replace.
Replace the new plate lining it up in one corner or edge.
You will need a steady hand putting the new plate back because it will probably have a high tack adhesive backing already on the plate, so once you place it down it will probably stick straight away.
DONT RUSH IT, GIVE YOURSELF TIME.
All will be fine, afterall you will probably look after your own car far better than any dealer will :thumbup:
PS.
I purchased the clear vinyl off Ebay, it comes on rolls various sizes, you just lay it on, trim out the shape you want, it instantly sticks but is easy to peel off.