Your best bet is the birth certificate of one of the children.
If you get William's birth cetificate, you should find Ann's maiden name. It is possible that they were not married on the island (the IOM IGI is almost complete and they do not appear, perhaps they were dissenters, or perhaps they eloped and married elsewhere -in Liverpool or Bristol).
In the 1841 IOM census, where the ages were often rounded down to the next 5( e.g. 23 = 20), the best bets for a Thomas Skillicorn born in 1822 are in Onchan age 18, District 3 page 8 entry 34 (same entry as Sarah age 10, John age 54, Jane age 40, Isabella age 14) or Douglas age 17 District 8, page 5 entry 25 - no other Skillicorns on this entry.
He may have already been on the mainland in 1841, but I doubt it if he married an IOM bride. In the 1851 IOM census there is only one Thomas in the age range. He is in Ramsey aged 26, District 4 page 26 entry 103 apparantly married to a Jane and with a two year old son named John and a four year ol named Charles.
The 1841 Onchan Thomas looks like a better bet.
P.S. all this info is thanks to Brian Lawson's indexes.