As they have all previously posted, there are a lot of variables in play with an autoloader firing a cartridge it isn't specced' for.
Shooting a .38 Spl. in a .357 Mag. revolver is easy: the rim holds it in place for firing and there is no set pressure needed to cycle the action. Autos? Not so much.
Shooting a .40 S&W in a 10mm has issues: the cartridge headspaces on the mouth, so if the extractor doesn't hold it tight against the frame the firing pin with either miss the primer or just bump the cartridge forward in the chamber. It could be a tight fit, which means a rod is needed to push the unfired round out. I'm not a fan of playing touchy with live soft-strike rounds still stuck in a barrel.
The springs are set for 10mm recoil, so if a lighter .40 is fired it may have enough oomph to cycle the slide fully to the rear to eject, cock, and strip a fresh round out of the mag....but I doubt it will do it reliably. (This goes for a Coonan .357 auto with the .357 spring in place. A .38 will fire because of the rim, but it wont push the slide back enough to cycle reliably until you put in the .38 specific spring). If you do put in a lighter spring, then BE SURE you replace it to the factory 10mm spring when you shoot 10mm or you will batter your Delta badly.
The mag is built for a specific length, so if the shorter .40 round shifts it may pop out early and tie up the slide on the return.
I stick to the mantra of firing only the caliber(s) the gun is made for, and I never load my own loads to the max, just to play it a bit extra-safe....others do with varying degrees of success. To each his own