I started western and have done it the entire time I have ever ridden, but I have always wanted to try english - right now the closest I have to english is jumping a small jump bareback, but boy it is fun!!
I think it depends on your horse, but I think any way can be natural for the horse. My horse is lazy, and he has done western his whole 22 years of living and has hardly and as far as I know never jumped a day in his life before me.
But I get on bareback and he jumps decently! He trips every now and then but he is still pretty good.
I don't think that the cues for english and western be different, either way you don't need any tools other than your body.
I don't think it would really effect your english riding.
I still psot the trot in western and jump small jumps with a western saddle, doing the best form I can. I only do english for fun, not like for shows and my horse will never be a real english horse anyways - and he is 22 and lazy.