If sideways is unreasonably difficult, run it with the hoses "up". It's not preffered, but will work.
How picky your cooler is about bleeding all the air out of itself depends alot on what kind of cooler you have.
The tube style coolers are much more forgiving about that than the Plate & Fin style (but the plate and fin are a better heat exchanger by far).
I have run a tube style cooler with the fittings down, but I would hesitate to try the same thing with a plate & fin cooler; if the cooler has the full flow.
If it's a partial flow, or bypass, I've done that too.
