That's more of a bargaining strategy question then I suppose? Do you feel lucky...? Maybe show them loan approval (in principle if necessary) and assure them that you can cover the rest from savings without showing any evidence of that?
In this situation, as a broker what I'll do is write a letter confirming that we've arranged a mortgage for Mr & Mrs X which has been approved and that I've seen evidence that, between loan amount and other funds available to them, they have sufficient resources to complete a purchase at €Y.
From speaking with my clients, I'll make sure that €Y is the bid and no more. If I have to increase €Y in a subsequent letter to accomodate a higher bid, so be it.