OP - as mentioned above - what you propose is a pretty minor alteration - like 30 years ago I was given a shoebox mostly full of IVI 7.62 NATO brass - it required a snipe on the handle of my RCBS JR press, but I reformed some of them in one pass into 243 Win. I think I did 50 cases, and do not recall losing any - but that was like "work" - making the neck go from .306" ID to .241" ID, or so - you would be trying to re-size much less than that. If I was to try that again today, I would probably anneal the cases and try for an intermediate step - like to 7mm-08 or 260 Rem, first - but I did not do either step back then. For many years, that was my only 243 Win brass - I must have reloaded and fired it perhaps 5 or 6 times. I used just ordinary RCBS-2 case lube on the case walls for the reforming - which should not have changed shape, much, at all. As mentioned above - just try a few and see what you get. It might help to lube the outside case neck walls, if you don't do that normally (which I don't).
As mentioned - your re-formed cases will likely be too long in the neck - so you will likely need to trim them to length and chamfer, before using them. You might also find that the case shoulder gets pushed back - perhaps 0.050" - so excess lube on case walls will likely "dimple" the shoulders as you resize them - I would expect a bit more "grunt" needed to press those shoulders back, compared to simply reducing the neck diameter. Then likely will have to fuss a bit to determine if your rifle's chamber will accept those re-formed brass with a .277" bullet seated inside the case mouth - perhaps goes to neck wall thickness, which likely varies one brand of brass to another.