It depends on whether you have metalcraft or not (because you've only listed two artifacts).
If you have metalcraft, you can legally activate Spellskite's ability, but the ability will do nothing. Spellskite has shroud, and you can't change the target of a spell or ability to an illegal target.
If you don't have metalcraft, you can redirect the spell as you normally could. Indestructible doesn't prevent damage, nor does it stop something from legally dealing damage. It just means that damage doesn't destroy that object.