Ordering software development without getting the source code can be called "project suicide". Allowing such things to happen is nearly the crime against the ordering company. Continuing to use the module without the source code endangers the product. If you not reverse engineer it and don't have any substitute, consider your whole project failed. No matter how much it costs, you should either reverse-engineer or develop this module from scratch, to have the source code of the software.
If you continue using this product without source code, you only put your main product close to collapse. You should not solve the problem you have posted, you should fix the whole thing and create and obtain the source code. Please see the comment to the question by virusstorm