Can I apply polymeric sand only on a x inches wide stretch where the patio joins the wall?
So you want to put 3 foot strip in width of polymeric sand over existing pavers? You will be OK with how that would look? I am just not sure how well such a strip will stay together over the long haul. 

I sure wouldn't do it, I would bite the bullet and pull up the pavers then regrade the base away from the house and put the pavers back.