The reason that S&W says no +P for .380 but it is OK for 9mm is because there is no SAMMI spec for .380+P. There is a spec for 9mm +P. Because of this, any manufacturers that market .380+P ammo can load it to whatever spec they want, or change that spec at the drop of a hat. That spec may be safe to fire or it may not. If SAMMI had a spec for it, then firearm manufacturers could evaluate it and decide if it is safe in their guns.
Having said all that, and keeping in mind that this is only my opinion, the .380 Shield EZ is a larger, more robust gun than something like a micro compact like an LCP. Also, I really don't think that ammo manufacturers would purposely make unsafe ammo, in this day and age of liability and lawsuits. Limited use of .380+P in something larger like the .380 EZ should be OK, just don't go hog wild and shoot nothing but +P. Carry +P hollow points for CCW and practice with standard velocity, only shooting enough of the +P to verify function. It will definitely accelerate wear, but I doubt it would catastrophically fail. Myself, if you need more power than .380, I think you should just move up to 9mm, not try to hot-rod .380. However, if the .380 is all you have and you can't afford another gun right now, I understand that, too. Just buy from a reputable manufacturer in case you have issues and be careful.