Can you transfer from Ukraine International airlines to British Airways at Kiev-Boryspil without clearing immigration (only hand luggage)?

So I'm considering flying Tbilisi-Kiev-London (TBS-KBP-LHR), with the TBS-KBP leg flown by Ukraine International Airlines (UIA), and the KBP-LHR leg by British Airways (BA)

I will not be able to have my passport with me, only my ID Card, which is accepted for entry/Exit in both Georgia and the UK.

Regarding transiting Ukraine, the IATA database says it's allowed with my ID "at Kiev-Boryspil on Ukraine International Airlines".

I understand why it's restricted to KBP (because that's Ukraine's only airport with airside transit), but what about it having to be on UIA?

If I had checked-in luggage, it would make perfect sense, but since I'm going Hand luggage only, my question becomes:

Is it possible to Transfer from UIA to BA at KBP without clearing Immigration? Since TBS has no BA desk (and I won't have Access to a Printer), can one collect the BA Boarding pass in the transit area at KBP?

I Need to know this in order to know whether I can do this route.