I was too quick in making an alarm. It appears waiting for newer BIOS is not needed. I took a chance and disabled false alarm notifications that were allowing me to enter BIOS via F1 key. And - surprisingly - did not loose a chance of entering BIOS at all
PC does accept my attempts to hit Delete key - it just has to be done at the very end of POST - right before OS load starts. Then, both - Delete and F8 keys (to choose boot device) work without a problem.