UA will most likely not be able to issue BPs on Vistara but will try to tag the luggage thru. Since you have to pick it up in DEL to take it thru customs that won't help you. There is no transfer counter in DEL, you have to give it to UK either in the small desk area after you come out of customs or upstairs in the general checkin area. Since your departure is rather late (>4h), the CISF will not let you go upstairs for checkin. So you have to get a room in advance at the PP arrivals lounge, 'allways' or at the HIX. If you manage to go upstairs and manage to give the luggage to UK, the only option there is the HIX, who have a courtesy phone available besides domestic security and pick you up to take you into the terminal hotel.

Reserving something in advance is the best thing to do, the transit facilities fill up fast.