I no longer recommend sending your kilt out to a dry cleaner to be pressed.
I recently took 3 kilts to my hitherto trusted dry cleaners to recieve a 'first press'. The regular person wasn't there and I must have spent 5 minutes explaining to the new employee what was to be done. As I turned to leave, she scooped up the kilts and dumped them on the floor next the steam table!
I explained that that was no way to treat $2100 worth of product, took the kilts back, went home and pressed them myself. I have no intention of taking any more work to them.
I encourage you to iron your own 'kit' rather than sending it out to a Dry Cleaner. You can do a better job at no cost other than the time spent.
If you DO iron your own kilt there are two more things to consider:
1) It's better to lift the iron off the cloth while the cloth is still steaming a bit. With experience you'll be able to safely press wool when it's dry, but the little bit of moisture provides a little bit of insurance. whatever you do, keep the iron moving!
2) Wool is a bit 'plastic' when it's wet - it loses it's elasticity and can be shaped. It is therefore REALLY important that you let the wool cool off and dry out before you start rough-housing with it.