Cutting Nails During the Thirty Days of Mourning to Avoid Barrier in Hand Washing

I am in the thirty days of mourning for my sister, and my nails are long. Is it permissible to cut the nails with a tool to avoid a barrier in hand washing?

There is no need for hand washing to cut the nails; it is sufficient to clean the dirt under the nails. The mourner may cut the nails with his teeth or hands even during the seven days.

Shulchan Aruch, Orach Chaim, Siman 161, Paragraph 1: "One must be careful of barriers, as anything that is a barrier in immersion is a barrier in washing, such as dirt under the nail not opposite the flesh, etc."
Mishnah Berurah there, s"k 3: "For example, if the nail is long and protrudes beyond the flesh of the finger, and the dirt there under this protrusion, most people are careful to clean them due to disgust, therefore it is a barrier, and this dirt must be removed before washing. And in dough, people are careful even opposite the flesh. See Yoreh De'ah 198, where several other things that are barriers are listed, but here common things are listed. And it is written in Aruch HaShulchan in the name of Sefer Chasidim that for this reason, it is proper not to grow nails." And it is only proper to cut the nails for hand washing (and even according to the opinion of Pri Megadim, Eshel Avraham, Siman 161, s"k 2, who holds that nails protruding beyond the flesh are a barrier, it is because they are meant to be cut. And here, in mourning, they are not meant to be cut and are not a barrier).