I wouldn't use that, too thin. You don't want it to cut the circulation off/cut into the plant.
I'm not a big LSTer like I said but search around there are a lot of topics on here about it. The big problem for most people when growing indoors is space, I don't really have that problem so I just let mine grow pretty damn tall. Yeah I'd say that if they are at the very bottom and are dying off it's because they aren't getting sufficient light, just pick them if they come off easy, if not then leave them, they will die eventually and then you can pick them off. If it's really bugging you, you can get rid of them, I just prefer not to unless I can barely pluck them right off.