Da, you also are playing into the hands of chabad, who routinely say that anyone against them is just against chasidus.
There are very, very few important people nowadays who are complete misnagdim. Rav yisroel elya weintraub was one such gadol, but since him and rav weinberg from canada….i don’t know of any others nowadays.
Whereas chabad painted rav shach as a misnaged to chasidim in general when he opposed their last rebbe, rav shach wrote letters and spoke openly about how he “can’t imagine klal yisroel without chasidim,” and how much he was machshiv them. Briskers often marry chasidishe women; the whole premise is ridiculous.