I have a soldering iron which allows the use of exchange-able tips, however I am unable to get certain tip types for my iron. Can I get a tip designed for a different iron if I match both the wattage rating and barrel size? It's a 50W iron with temperature control.
The answer to your questions is a 99% yes, possibly no in very rare cases such as if your iron is a specialist type that uses inductive heating or other less common method innolving specialist tips (in which case you can still probably get some clone tips)
Anyway, my experience with this is a positive one - the most extreme case was ages ago when we didn't have enough soldering stations here with irons/tips for some SMD prototyping (different fittings) I used a couple of Pace hoof/micro-wave tips I had lying around with an el-cheapo iron for drag soldering TQFP ICs for a day or two until a more permanent solution arrived. The tip didn't even fit that well (it was a nasty little 35W thing with a screw to hold the tip in) but it got hot enough and the results were very good.
Apart from that I've used various tips from eBay (Hakko/clone/? types) that fit my very common size of Hakko-clone iron. As Mark mentions, as long as the fitting dimensions are correct (and the size/mass isn't radically different) then all is well.
So don't worry if it doesn't say "for use with ", just make sure it will fit okay. As mentioned above make sure it's not some specialist tip with some kind of heating element inside (although you will probably be put off by the price before you get to the point of checking this...)
As suggested, taking a few pictures and posting measurements may help get you some recommendations on suitable tips and where to source them.