Finance query – pay in cash; mortgage later?

Hi

I’m in New Zealand on holiday at the moment and have found an a promising potential investment property up for auction. Unfortunately the auction is within the next couple of days and settlement is only a few day after that. If I am the sucessful bidder, I will have only a very limited time to organise finance. I don’t want to borrow from a New Zealand lender and want to use the equity in my Sydney home to pay for the investment property. My problem is this: I won’t be able to organise the valuation etc required to borrow against my Sydney unit before the settlement date and the only way I could pay for the NZ property is to cash in some other investments (I don’t have any other investment propertys).
My query is this – Can I pay for the property in cash (from my cashed in investment as above) and then somehow use the investment mortgage (from my Sydney unit – organised after the settlement date) to put this against the investment property in New Zealand and treat this as a normal geared investment. Or, is this not even remotely possible as I guess the settlement paperwork will show this as paid in cash (no mortgage)? Hmmm… I’ve just read this through again and probably haven’t explained it very well – hope you can understand what I’m asking.

Cheers

Tim