Charter Captain reported the undocumented air transport of Hazmat cargo which was mistakenly left on board at the previous stop over. After conferring with Dispatch the flight was prepared for a speedy departure to a suitable alternate which could accommodate the Hazmat cargo.

Narrative

US Military ordnance in ZZZZCause…that's simple; nobody unloaded a belly full of Boom-Boom's" on previous flight? As soon as we arrived the loadmaster/station rep came up to me and said we have a problem; being that I just arrived I sighed some relief that it wasn't my doing; that I knew of. The rep showed me a picture of the "special cargo" located in the bellies. We looked at each other pausing and I stated that's gonna be a problem. I asked her if the door was closed to the belly? She confirmed yes; they closed it as soon as they opened it. I told her to keep it closed. I had her confirm what we had; how much and reviewed the previous flights manifest. I tasked one of the First Officer's (FO's) to get the previous flight inbound to ZZZZ1's flight docs so we had an accounting of what should be down there. I contacted the Duty Pilot; he patched me in with Dispatch and told him the current flight plan probably wouldn't work given it's routing up and through a waterway. I asked him if he was working up a 'special routing' option departing straight east around Country and up towards ZZZ; he said that was his thought as well and wanted to check with me if that worked. The remainder of the preflight was normal beyond that. We got notification the company was going to load cargo; we had one FO activated to operate with us so we could have a four crew compliment; we had one jump seater we could not accommodate due to restrictions. We had all copies of previous exemptions; and restrictions; it was left to the company to insure permitting. When we got our revised flight plan I noted the Country overflight permit; and reviewed the load plan for location of ordnance. Flight progressed normally; departed a little late due to loading and landed in ZZZ parking on XX away from other aircraft.Suggestions: A Company Loadmaster needs to be on these flights. I've had other issues lately when we did not have a Company Loadmaster onboard. I would also suggest making the "small font" check of the FMC's "sensed cg" and compare that to the weight and balance cg. A gross error would have absolutely been detectable on a load that far forward on CG especially when ballast fuel may have been added. Also showing how to use the AOA system as a cross check for calculated target speed vs "AOA target" would help crews identify abnormal handling conditions when on approach which are effecting the flights handling characteristics. This harkens back to "wet cargo" or anytime actual cargo weight is subject to doubt. When setting final approach target speed; it should approximate amber and +10 kts. on a 737/757/767/747-400 or amber and +15 kts. on a -8F/777/787. AOA target also protects crews from low energy approaches and mitigates hard landings in a -8F regardless of flap setting or weight…. FWIW"