You might be able to reclaim the VAT but you'd need to register for VAT either as a Limited Company or as self employed. Irritatingly you cannot offset the cost of your type rating against income for tax purposes in the UK. I know people who have done it, but if HMRC catch you, you'll have to pay it back and may be fined. It's not an allowable expense under UK law.
You need to see an accountant / tax advisor really. It all depends if you will be employed by Wizzair or work for them as a contractor.