If a hacksaw is too big, sometimes you can fit a hacksaw blade into the space with a holder. The problem with using a blade holder, though, is that you always end up bending the blade. Sure, you can install the blade so it cuts on the pull stroke, but it still can and will bind on the push stroke. When the blade stops and your hand keeps going, something’s got to give.
One solution is to use a close quarters saw from Lenox. It isn’t much bigger than a hacksaw blade in a holder, yet the blade is fully supported by an aluminum frame. You can pick up one of these saws for starting around $12. Though a downside is that you need to buy special blades, at least they’re pretty cheap: You can pick up 10 for about $10.