Tax implications of paying buyer outside of 1031

[Ramaiyer Ramesh]

A prospective buyer wants to get a non-confirming loan (due to attractive 7 year rate). But they want to pay 10K less in purchase price as we are splitting some remodel cost. 

If the purchase amount is reduced, that will push them to a confirming loan. If they put less 10K then it will kick in PMI. Both scenarios the buyer wants to avoid. Assumption there is removing PMI needs refinancing and in this economic scenario, buyer might end up in a higher rate.

I want do 1031 exchange from the proceeds of this sale. If I pay out of my pocket the 10K,  can I claim it as part of 1031, so I don't pay taxes ?  Any advise for me ?