You can use Spell Strike in any situation you could use a touch spell. But charging is a full round action, You cannot do anything else but charge.
The only issue i can think of though is wether you might accidently zap your horse while steering it.
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From what i can see with the feats mounted skirmisher allows you to take a full round action atop your mount. To use spell strike without spell combat you only need a standard action atop a mount witch you can do in place of a full round action. As for the mounted charge it normal grants only one attack but as you read mounted skirmisher allows for a full round action. Both casting a spell (standard action)by itself (spell strike allowed) and spell combat (a full round action in itself) fit into the fra space. So as I read it i would say yes. That is three Feats to do that tho...... Are you really mounted that much.... your a halfling arn't you...?
The free attack granted by a touch spell can be taken anytime during the round, so you can cast, move, attack.
If you were to cast, have your mount charge, (using your mount's full-round action,) you could the deliver the spell with your free attack when your mount has completed it's charge. Since you mount charged, you would also get the +2 to attack and -2 AC.
You don't need to have Mounted Skirmisher to do this.
Remember that Mounted Skirmisher does not allow you to take a full-round action after your mount has moved, it allows you to take the full-attack action.
That means you can't use it to make a full-attack and cast with Spell Combat, and you likely can't use it with Spellstrike as casting the spell is usually a standard action. If you're holding the charge, or cast a spell as a swift action, then you could use mounted skirmisher to move and deliver the spell as part of your full-attack.