canopy is just a wrapper on top of Selenium Webdriver. You can access the current browser/driver with browser or core.browser like you show above.
I believe that this should work for your first problem:
browser.Manage().Cookies.DeleteAllCookies()
For your second question, this should give you a string list of values for non secure cookies
let httpCookieValues =
browser.Manage().Cookies.AllCookies
|> List.ofSeq
|> List.filter (fun cookie -> not cookie.Secure)
|> List.map (fun cookie -> cookie.Value)