But they aren't Skirmish; that's like saying, "Well, a Scout gives me Skirmish, which is basically Sneak Attack, so my levels in Rogue and Scout stack for the purpose of my Sneak Attack dice."
Seriously, Swift Surge doesn't even add to the same things that Skirmish does; you're getting +2 attack rolls/+20 Base Land Speed, not +2d6 damage/+2 AC, as you would with Skirmish.
Unless your talking about the extra damage it gives you, in which case that still ain't Skirmish; you get +6d6 extra damage when moving 20', and you get only 3d6 after moving 10'.
Sure, at the end of the day, all that matters is that it adds damage, but I am a stickler for terminology.
So I'm not really having a problem with the build (though you need 20' of movement, which is hard to get in an enclosed room).
And your DM should definitely NOT allow you to advance Mystic Ranger levels with Swiftblade; Ranger's casting is Divine, no matter what.
Sword of the Arcane Order allows you to prep Wizard spells in your Ranger/Paladin spell slots. Rangers cast Divine spells, and spell lists are not inherently one type of casting or the other.
Seriously, check Dragons (some cast Arcane spells off of the Cleric spell list), or Divine Bards (there is no statement that "if you use this variant, the Bard spell-list is now Divine"; it just says that Bards now cast Divine spells from the Bard spell list.).
So, yeah, Sword of the Arcane Order gives you those Wizard spells in a Divine manner. Sorry.