no uber to boardwalk then walk to international gateway. it is so close, lol. BWV is my home resort and I have taken many many trips there over the years. I have maybe taken the boat once or twice, only if it was right there waiting (it is the last stop on the run on the way to Epcot). They would drop you at the front side of the resort. You would come through the lobby straight through and exit out the back to a big porch, walk down the stairs (or you can take an elevator down) and then walk out to the boardwalk, make a right and follow it around. Maybe 10 minute walk and I am a "stroller," (both the kid and I walk slow lol). it is up a hill a bit as you cross over the canal but otherwise it's a nice and easy walk.
here it is on google earth. The star at the bottom is where uber will drop you. the arrow on the path is the little uphill section (it is actually approaching that bridge that is uphill). the circle is around the international gateway (admission point for Epcot) and the first star on the bridge is my favorite viewing location when the second star (a little peninsula down below) is taken. the second star is where the illuminations dessert party is held I believe. Hope that helps visualize it.
and actually beach club might even be closer. But boardwalk is a nicer walk (less wandering through the resort and some time on the actual boardwalk). But BW is a "destination" so they will never question where you are going through the gates. that's why it is my go-to when I am going to epcot, lol.
AND you don't have to uber. if you walk to MK you can get a direct bus there. Basically the less often you have to rely on disney transport the better. Every transfer to another transportation introduces another worst case scenario. So I would probably walk from contemporary to MK, take the bus to BW and then walk from there and it should take less than an hour even worst case bus scenario. (I always give 40 minutes worst case scenario for any one leg of transport). If you uber it it is probably 15 min direct from contemporary to BW or BC.