On my installation, I do not have a function “Copy as quote”. If you have a literal “Copy as quote” command on your system (check in the command palette), then it may have been provided by a plugin. As soon as you have the command there, you should be able to assign it a shortcut key with the standard procedure.
There is a standard function “Toggle blockquote”. That could be bound to a hotkey. Then, pasting a paragraph as a quote would involve just two hotkeys. When multiple paragraphs are pasted, they first need to be selected in order to turn them into a quote.