Yes, finally I really did grabbed cookies through dev panel and pasted it in http settings and it worked without user:pass even. But it worked only with the query which I have already worked with through the site. E.g. https://www.merchantwords.com/search/v1/us/strength%20bands%20for%20pull%20ups/sort-highest - I worked with is through the site directly, then typed cookies in and excel fetches data.
If I do new query through excel, I apparently need new set of cookies because with a new query the fetching fails - website doesn't "see" me as logged in.