The key to many, if not most, of these proposed 40-to-10mm "conversions" is the magazine - that is, whether the stock .40 mags can accomodate, or be "fixed" to reliably accomodate, the longer COAL of the 10mm. Since most can't, there it ends unless all you want is a single-shot 10mm.
Apparently, the mags for Sig's .40S&W M2 Mauser pistol have a metal spacer or plug which can be removed, making it compatible with holding and feeding 10mm ammo. I wasn't aware of this. (See? You learn something new everyday on THR.
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Once you've got your hands on .40S&W mags that will work, or can be made to work, with the 10mm cartridge, the stock .40 barrel needs to be reamed out to 10mm specs. This is relatively easy and any competent 'smith should be able to do it.
The "10mm" HK.
Yep, it's been done, apparently. A couple of years ago on pistolsmith.com, a poster from Alaska described how he "converted" a full-size HK .40 to 10mm. Same basic process. He started with the mag. HK uses a dedicated .40 mag without a spacer, so the 10mm cartridge won't fit and the mag can't be readily altered. End of story, right? Nope. The poster was in a gunshop one day with his HK and got creative, experimenting with various mags from different gunmakers to see whether their .40 mags might fit in his HK .40.
Bingo! He discovered that a hi-cap .40 Para-Ord mag (which will also hold and feed the 10mm cartridge) fit nearly perfectly in the mag well/chute of his HK. He had to cut a mag catch opening on the off-side of the Para-Ord .40 mag to get it to lock-in tight with the HK's mag-catch latch, but apparently that wasn't a big deal. He was able to get several Para .40 mags working reliably in the gun. Next, he had the barrel reamed out to 10mm. Then he put stronger Wolff recoil and firing pin springs in the gun, and was soon out shooting hot 10mm loads. I recall he commented that his "10mm" HK shot perfectly to point-of-aim with the factory sights.
If you're interested in more details, you might do a search on the Pistolsmith sight, as it was discussed there more than once. In fact, IIRC, several posters have tried this conversion.
Good luck.