In OTL Britain's claims vis a vis the boundary dispute angered the American public, but for several months the British cabinet underestimated the depth of American opposition to their position, before finally agreeing to arbitration in January 1896. What if they had refused? The consensus in older threads seems to be that US-UK relations would sour but that a third Anglo-American war was unlikely to immediately break out, but would there be an Anglo-Venezuelan war, or would it just be a geopolitical sore spot?