Hmmm. Running it farther into the die than intended will set the shoulder back. Not a safety issue as it headspaces on the rim, but with all the extra working of the brass (firing/sizing cycles) it may cause increased neck/shoulder splits. Annealing would be to your advantage. That's not to mention greatly increased case body stretching on subsequent firing leading to early case head separations, which would be the far greater detriment. Perhaps do that trick just once and then neck size only thereafter?

This being a single operation on once-fired brass fired in another rifle, I wouldn't worry too much about shoulder setback and case stretching.  After all, it's not the intention to do this every time, just for fitting the once-fired brass to the chamber.

The only sizing die I have ever owned that is a perfect fit when full length sizing is a custom RCBS die that was made for my 7mm/303 EPPS High Wall.
You should measure a fired case and with small increments lower the sizing die until it is the same shoulder measurement of the fired case. some people with bolt guns like to give a bit more length so it gives a bit of fell when turning the bolt down.
I have found that with a small BSA Martini that if you neck size too often you can have trouble with the weak extractor.
I had trouble writing this as the little thing that shows where you are on the page had vanished, Just had an update on my apple computer and wondered if that was the problem or a problem with the web page? on re-reading this I notice I have put a capitol J after the comma and to correct this I would have to delete every thing up to this so please excuse this.

Oneatatime stated that he had not experienced problems with his 3 K HORNETS. Part of the reason may be that by rechambering to K HORNET you have minimized or eliminated part of the problem with the Hornet case, such as case stretching due in part to very thin case walls, which can lead to case separations. Savage mod 23 Hornet rifles with rear locking lugs are notorious for stretching cases, again, due in part to less support from rear locking lugs. Those that I had and rechambered to K hornet, helped with the problem, along with lighter pressure  loads yet standard hornet velocities in the K chamber. I now have a K hornet on a C Sharps model 1875, and a Winchester 54 Hornet, neither have given me any problems. The most simple solution is to not oversize, and not try to make a Hornet into a Bee.

My K Hornet was in a Thomson Center Contender carbine, break open action & good extraction. While not a a “K” similar case 25/20 is in a Marlin 1894 Lever Action. Extractor barely larger than typical .22 LR extractors. Had to carry a cleaning rod to knock out stuck cases. 

Fix for the Marlin was proper sized case & I suspect same will be true for your BSA. KHornet case in my TC never showed signs of stretching. After the first fire form & trim all case work done with neck sizer die.

Agree with rkba don’t hot rod the cartridge for best result.

Boats