there is no easy way, it is a pain in the a$$!! you have to try and remove the plastic ends, they slide out a bit, i sprayed a little WD40 inside, under the trim pieces, if you look from the back of the neon, where the key hole is you can see where the trim piece clips under there, unclip it and lift it up a bit in the front and you have to just slide it off, its not easy!! requires patience, this took me a couple of hours and i had to keep walking away or i was going to fling it!! be carful if you try it, try not to bend the trim piece, and there is also a black wire in the back going thrrough the area of the keyhole, this is attached to the front trim piece with a teminal, it is to ground the trim piece. if it pulls off its okay, you can just put it back on after and run it through on the new neon.
The reason i am removing them and just not painting the replacement is incase my replacement is from a base, i used to work at a bodyshop and from personal experience i know that you can not succesfully paint chrome, i dont care if its metal or plastic chrome, nothing ever sticks to it right. so if you paint a chrome one, within a couple of years you will need to repaint it.