If you're going to edit your movie, I
strongly suggest against it. Let's face it. You're not Shaolin Productions. Unless you've got a really decent amount of experience, you shouldn't edit movies. Not even if it's to add music to it. Timing is really difficult, and it takes a long time before you're able to properly pull off such mixing. Cutting out parts of the game where you're waiting is
not a good idea. Cutting out parts of the game where there are status screens that remain visible for a long time, but can't be skipped, can be a good idea in very rare cases (e.g. the "new weapon" screens in Rockman 2), but shouldn't be done in tool-assisted speedruns. Cutting out actual gameplay is completely out of the question.
Your run will be "different" than conventional runs, but consider if your proposed changes will actually be for the best. Wouldn't your run end up like a cheap fragvid on
own-age.com? There are many people who try to enhance their videos, but only a very select few who are able to do this and at the same time entertain their audience. Music and other editing makes your video more personal, and thus, there's a large chance that your potential watchers will be turned off because they can't identify themselves with it. If you make a speedrun, whether tool-assisted or not, you're best off positioning yourself for people who enjoy watching runs without these sort of additions, and prefer the original soundtrack of a game over another layer of music added on top of that.