The easiest and probably best solution is to install an outlet to plug the converter into.
It may be possible to safely splice the wires you have together (cutting off the plug on the converter) as well, depending on the exact setup. It may also be impractical to do that safely and properly.
If you're not sure of the wiring, I would strongly urge you to hire or get help from a qualified person. It's not particularly complicated or difficult, but not doing it properly can create a significant shock and/or fire hazard.