Goodaltgamer: It has been said over and over again in this forum: Do not delete your cookies ;)
That shouldn't trigger captcha anymore (it did at some point a week or two ago, but it seems GOG changed that back). It will trigger two-step authentication though, in case you have it enabled. For instance I logged in to my account now on this Linux PC with Firefox, which does clear cookies every time I exit Firefox, yet I don't get captcha.
I don't even know when captcha comes at this point. I know I never see it (ever since GOG changed it back). Does it come after a number of failed logins, or if there are many people logging in at the same time to the same account, or what?