Demonus, as Arabella said, plan on raising Tinkering skill on the same character that is working on Remove Trap skill. Your only alternative to this is to raise Tinkering skill on a separate character at the same time and switch between the two characters as you go.
If you do the Tinkering skill on the same character as Remove Trap, you can probably get away with just using one box that you trap and disarm repeatedly. However, if you have the two skills on separate characters, you will most likely want to work with a much larger number of boxes. Put the keys on keyrings. Each keyring will hold 20 keys, so perhaps do either 20, 40, or 60 boxes.
Try to keep your Tinkering skill at least 5.0 but not more than 15.0 points higher than the Remove Trap skill. I did one time manage to GM Remove Trap with my Tinkering skill raised only to 92, but I think your Remove Trap gains will come a lot faster if you take the time and use up the ingots to get to GM Tinkering. Also, if you plan to make faction traps, you need to have at least 90 Tinkering skill to make them (ignore the fact that the tinker tool gump shows a lower skill level).
As mentioned, you must have at least 50 Lockpicking and 50 Detect Hidden skill before you can purchase Remove Trap training. I believe you can manage to train Remove Trap all the way to GM with only 50 Detect Hidden skill. However, if you have any plans to actually use the skill in factions, you will need enough Detect Hidden skill to reveal a faction trap before you can disarm it. I think you start being able to reveal faction traps (if your character is in factions) when you hit 80 Detect Hidden skill. (Could be 90, though. Can't remember.) You can train Detect Hidden skill off your trapped boxes as you go. Or hit up any place that has large amounts of static trapped chests/boxes and use the skill on them. The Treasure Hunters of Britannia section of the main Stratics site (
http://uo.stratics.com/thb/index.shtml) has a lot of information about where to find chests of varying levels and types (i.e., static versus spawning).