The scenario as presented by you is totally different from position faced by OP on this issue. It appears that you currently have a joint mortgage on the property and intend paying this off fully. Then presenting a case to the Bank for a new mortgage of 150K.
The Banks are not obliged to take her name off the mortgage unless that is specifically part of the separation agreement (AFAIK). This is your first port of call. From your own perspective I would advise a 2 tier approach. First would be to get the mortgage transferred to your own name. Assuming that your repayment position is good and with 60K savings the Bank may be satisfied to do this voluntarily. If not then you may need to look at the issue of the separation agreement. If they agree then you may be in a position to retain portion of the 60K savings in return for taking over the full mortgage and therefore new mortgage requirement could be reduced.