Every second is a fulfillment of a Mitzvah D’Oraysa. The Tzitzis themselves have no Kedusha as we see we can take them into a bathroom, unlike Tfillin or a sefer Torah. If so, what’s the problem with having a “shvitzy” pair and washing it like we do to our T shirts and sports clothing?
The Gra lamented on is deathbed that here we can fulfill Tzizis for a few kopeks and in the next world we cannot add one Mitzvah for all the money in the world. While alive we can…….. should’t we?