Why is your wife not on the mortgage application? Even if she is a student and has no income, she can be on the mortgage and on the deeds. There is an issue being on the deeds but not on the mortgage as, technically, if the lenders allowed it, which they won't, your wife's interest in the property might not be captured. That is a very simplistic explanation but lenders will not allow you to unilaterally nominate your wife's name on the deeds but not on the mortgage.
Talk to your solicitor anyway at this stage to get more case specific advice.
mf