Would takes a verb object. Here "we would " is an elliptical version of "we would spend."
The statement is an implicit type 2 conditional. (rephrase) "Sunscreen emboldens us to spend more time in the sun than we WOULD SPEND otherwise (= if we didn't use/have sunscreen).
Here, the modal could can replace would with no significant change in meaning. Like would, could takes a verb object. (rephrase) "Sunscreen emboldens us to spend more time in the sun than we COULD SPEND otherwise (= if we didn't use/have sunscreen).