Let me ask you a couple questions in return?
1. What are you hoping to accomplish with this cross breeding? By that, I mean are you trying to increase production (more eggs, more meat on a bird for food, etc), trying to develop a more hardy strain for your area, working on presentation (EG pretty birbs), etc?
2. If you have one sick bird right now, is it wise to try and breed him any time soon vs keep him isolated until he's fully recovered or ends up in freezer camp?
3. Have you looked into the traits of the birbs in question to know what kinds of results you MIGHT see based on genetics?
Once you can answer all of those questions for yourself and be comfortable with them, you'll have a good idea of what you're looking for and whether of nor your current flock can get you there. That will tell you whether or not you should or should not in general, and the overall condition of your birbs and any genetic traits they might pass on from this experiment will give you the rest, I'd think.