Shade - the key part of the mortgage, from a registration perspective, is the charging clause itself. For example 'The Borrower hereby charges the property...." - the borrower will be defined and must include all the registered owners for it to be registered as a legal charge.
If you can't achieve that then the lender would be looking at protecting their charge by way of a
Notice or Restriction but I'd expect them to be aware of that and already guiding you, through the conveyancer, as to what type of security they are offering etc
These aren't Qs HMLR can answer and advise you on - if you are looking for an alternative from what the conveyancer/lender are advising it's them you need to be discussing options with