OK, done deal, thanks for the info

If it helps anyone else, another tip I thought of while doing this - my bulkhead connector is installed in the car, so makes it impossible to get to both sides at the same time (i.e. to insert the screwdriver and to pull on the wire).
So...I got a spare male terminal in a pair of pliers, pushed it in to the female in the bulkhead connector, and also inserted the screwdriver, then pushed. It worked a treat, hope that helps someone else.

While I'm at it, another question.
The new female terminals I have are the ones in the picture below, slightly different from the ones I have just taken out. They grip the male with the big sprung blade rather than the alternative 'curled edge' terminal that is in the car now. They still have the retaining tang on the back.
Any reason why these would not work??