Why would it? Very easy to argue resulting trust with your wife as trustee for 50%. Your position would be even weaker if you had a joint loan.
See Cummins case and there are many after it.
There may be little choice then.
Did you know that even though the title is in her name half would probably be up for grabs if you were to go bankrupt?
It might be better asset protection to keep the loan as is. Cash readily available and a mortgage may deter creditors from taking legal action, to an extent.