Swift Hunter into Horizon Tripper, viable?

[G.Cube]

How well would it work out?

Would the teleport activate my skirmish damage?

[Eldariel]

How well would it work out?

Would the teleport activate my skirmish damage?

Not well. Horizon Walker's ability takes a standard action so you can't actually attack the same turn. Not to mention, even if you get around that by Quicken Spell-Like Ability, Dimension Door (http://www.d20srd.org/srd/spells/dimensionDoor.htm) has this funny clause:
"After using this spell, you can’t take any other actions until your next turn."

[G.Cube]

Not well. Horizon Walker's ability takes a standard action so you can't actually attack the same turn. Not to mention, even if you get around that by Quicken Spell-Like Ability, Dimension Door (http://www.d20srd.org/srd/spells/dimensionDoor.htm) has this funny clause:
"After using this spell, you can’t take any other actions until your next turn."

Darn, is there another non-cheesy, non-item based way to make a teleporting skirmisher possible?

[Eldariel]

Darn, is there another non-cheesy, non-item based way to make a teleporting skirmisher possible?

Do you want to specifically use Skirmish-ability or is just a character who fights in that style without the ability of that name okay?

Either way, best ways to get actually usable in-combat Teleportation are either Swordsage (Tome of Battle), Incarnum (Magic of Incarnum), Psionics or Arcane Magic (Divine works too, but less efficient). Swordsage is probably the easiest of the bunch. They can be combined with Skirmish-ability though that's rarely efficient and they all have their own ways of getting damage anyways so they don't really need it.

[G.Cube]

Do you want to specifically use Skirmish-ability or is just a character who fights in that style without the ability of that name okay?

Either way, best ways to get actually usable in-combat Teleportation are either Swordsage (Tome of Battle), Incarnum (Magic of Incarnum), Psionics or Arcane Magic (Divine works too, but less efficient). Swordsage is probably the easiest of the bunch. They can be combined with Skirmish-ability though that's rarely efficient and they all have their own ways of getting damage anyways so they don't really need it.

For the purposes of this guide, I'll say specifically skirmish, can it even activate of any sort of teleportation?

[Eldariel]

For the purposes of this guide, I'll say specifically skirmish, can it even activate of any sort of teleportation?

Well, errata on Skirmish says the following:
"She deals an extra 1d6 points of damage on all attacks she makes during any round in which she moves at least 10 feet away from where she was at the start of her turn. The extra damage applies only to attacks made after the scout has moved at least 10 feet. The skirmish ability cannot be used while mounted."

So, as long as you're not mounted it should work okay provided you've moved 10' away from your starting location.

All the aforementioned power sources can intermingle with Skirmish though of course, you need a significant number of class levels for any significant amount of Skirmish (5 for Improved Skirmish at bare minimum). Jaunter [Expedition to the Demonweb Pits] + Quicken Spell-Like Ability would work too though only 3 times per day with the Teleport; Dimension Door has the same annoying restriction as ever.

[Shloogorgh]

you could go into crinti shadow marauder for shadow ride and shadow pounce. Use shadow ride to teleport and activate shadow pounce, then as a free action make a ride check to dismount to qualify for skirmish. It's a free action to mount as well, so just rinse and repeat

[Chronos]

Four levels of the Telflamar Shadowlord PrC, from Unapproachable East, gives you an ability called "Shadow Pounce". Basically, whenever you use a teleportation ability, you can immediately make a full attack right afterwards. You also need some source of Sneak Attack to qualify for the class.

The Sun School feat from Complete Warrior provides a similar benefit, but only a single attack, not a full attack. You need Flurry of Blows (which probably means a monk dip) to qualify.