According to Rav Schachter, even though normally one is not allowed to wash himself, even just his hands on Tisha B'Av, if one feels the need to wash his hands on Tisha B'Av this year to protect against Corona, as per the instructions of the various health organizations (ie Ministry of Health, WHO, CDC, etc) would be allowed to.
However, he would only be allowed to if he strictly adheres to all the rules of the health organizations that were put in place to protect against the virus, including masks and social distancing. if one is flippant and is not careful about the other rules, one cannot say he needs to wash his hands as protection against the virus. If someone is disregarding the other rules of the CDC, he cannot insist on this one, and washing would remain prohibited..
I might think even though a person is an anti-masker, he still might see the importance of regularly washing hands, and for him that could be allowed (though not if he were only doing it on Tisha B'Av but isnt careful about it the other days).
Rav Schachter is taking an all or nothing approach with following the CDC rules. If you find the advice of the CDC valuable, keep it all or don't use them as your excuse. source: YU Torah