In regards to Island of Blades, you'd need to dip Swordsage for it, which might not work out so well for you. As far as I know, RAW says that you can use it while mounted, unless that was explicitly denied in a FAQ or bit of errata that I haven't heard of. IIRC you're planning on doing Ranger/Rogue, correct? It's already questionable since you've burned your 'dead' level in Rogue on Ranger 1. Something like a mounted Rogue planning on doing Rogue 19/Swordsage 1 could make pretty good use of it, but taking it instead of a level of Rogue now would cut into your peak sneak attack dice as well as delaying your level advancement.
Basically, you're dipping both Swordsage for increased reliability on your precision damage, but the fact that you're multiclassing Ranger means that your Sneak Attack is going to be sub-par compared to a straight Rogue already, and IMO it probably wouldn't be worthwhile dropping it further.
As far as the potential Rogue/Ranger breakdowns go, there are a couple points which balance class features about as well as possible for this combination: Rogue 9/Ranger 11, Rogue 3/Ranger 17, Rogue 15/Ranger 5, and so forth. I can't really see a good balance to insert Swordsage 1, except maybe into Rogue 13/Ranger 6/Swordsage 1 or Rogue 17/Ranger 2/Swordsage 1. In addition, since you're doing both archery AND TWF, you're already going to be feat-starved unless you burn all of your Rogue special abilities for extra feats or take Ranger all the way to 11th level for the combat mastery tree, which diminishes the possibility of you using feats to boost your sneak attack damage. Basically, if you were going to do straight Rogue I'd say to go for it; if you're planning on doing more than two Ranger levels, don't.
Pre-emptive edit: After reviewing the rules on mounted combat and everything I could find regarding it online, I haven't found anything that says that you shouldn't be able to use Island of Blades with your mount while mounted. That, and since the fact that rules for other circumstances allow both you and your mount to attack, provided the latter has a way to attack, I'd say you're probably good.
As for Hide and Move silently, unless you intend to spend literally all of your time mounted, you probably should. It's not like you have a dearth of skill points as a Rogue with a +2 Int modifier, after all.