Correct on use of the piece of brass rod
As for the nipple threads it can be iffy getting threads on a modern mfg. nipple to fit hand cut vintage threads properly but occasionally I've gotten lucky.
If the new nipple isn't a tight fit but if the outside diameter of the nipple treads are a tight fit you might be able to chase the threads with a 7.75mm tap & get that to work. Treso makes a wide variety of nipple thread sizes so won't be a problem coming up with a safe & reliable fit.
You may already have experience with what I state below, if so just ignore.
If your original nipple is corroded & frozen solid, soak the bottom 2" of the breech in a 50/50 mixture of auto transmission fluid & acetone overnight & that should do the trick, is the method I've successfully used for years. With real hard cases you may need to apply heat to the breech plug around the nipple.
On really stuck nipples I often use automotive ignition wrenches in metric or American sizes or cut a slot in a 1/4" drive socket to get the best fit as some nipple wrenches don't hold up well.
Once you have your barrel slug measurements taken I'll do my best to make a RB mold size recommendation. The original Jaegers I've rifles owned & shot all had deep rifling & required cotton pillow ticking with a high thread count to shoot the best groups. Likely won't find patches' on a dealers shelf, but take your micrometer to the fabric store & get a couple yards of the compressed thickness material you require & punch them out with an Arch punch on a hard wood or nylon surface after washing a couple times to get the sizing out.
Patch tip; I place stacks 50-75 patches & run a piece of nylon thread through the center with a needle to hang from my hunting bag. A knot at the bottom will prevent lost patches & allow for fast loading.
Happy trails !
Relic shooter