Question about Tristar Ac-5531

Agree. Witht the above mentioned untit it wouldn't make sense since the warm air needs to exit...

There isn't any true air conditioner without the exhaust air hose. You could find ones with water but they won't cool anything.
I would recommend you find a split air conditioner with a smaller tube (just the coolant).
And if you go for one with air hose take one with input but also output as it's way more efficient