The least amount of outdoor exposure would be taking a taxi to the Beach Club, walk through the length of the Beach Club lobby, past the Marketplace store and Sandcastle Club and follow the signs to the small quiet pool, walk around the perimeter of the pool and out the gate. It's the closest point from a resort to the IG.
The least amount of walking would be by taking a taxi to the Boardwalk Inn, go through the lobby, out the opposite side, walk down to the Friendship Boat Dock and take the boat to the IG. You'll be outside more, but you'll walk less and the boat goes directly from the BWI to the IG.
Walking from the front of Epcot to the WS is not a short walk. You could hop, skip and jump between buildings, but if you're looking for the least amount of walking and/or outdoor exposure, I wouldn't recommend this.