For one whose custom is to recite Birkat Ha-Mazon while holding a cup of wine (or grape juice) and one who is adopting the custom to refrain from eating meat during shavua she-chal bo Tisha b'Av:

Does the requirement to use a cup trump the prohibition of not consuming wine, or should one continue to bentch al ha-kos?

For one whose custom is to drink wine (or grape juice) after reciting Birkat Ha-Mazon and to refrain from eating wine during shavua she-chal bo Tisha b'Av:

Does the requirement to use a cup trump the prohibition of not consuming wine, or should one continue to bentch al ha-kos?