For someone who was trained on a Beretta M9 or a 1911, I can understand the discomfort of having no external safety. For a person like this, it does seem questionable to carry a gun with a round in the chamber, and risk it discharging unintentionally. However, the trigger on a 1911 or a M9 in SA mode is a very, very different trigger than on the SDVE. I would never carry one of these two guns (1911, M9) with a round in the chamber and the hammer cocked...unless the pistol was also "locked" (as can you do with a 1911; the M9 will decock, unless I have completely forgotten the action...I haven't owned one in a while.)
There are people who advocate the "Israeli draw" method of carry to address just this concern. (That is, the pistol is carried without a round in the chamber, and the slide is racked as the pistol is drawn.) If you are going to use this method, I would suggest that you train extensively, until it becomes second nature, relying on muscle memory, and doesn't require you to "think" about your action. Even then, under stress, it may not go as smoothly as when you drill...but extensive drilling may help compensate for stress reactions, if you have done it to the point that it over-rides any other conditions.
However, as others have suggested, the SDVE pistols have a purpose-designed heavier trigger to alleviate two possible concerns: one being an accidental/negligent discharge; and the other being very similar, but involving firing unintentionally when you are holding on a person. (There are many that also say you should never point a gun at another person unless you intend to shoot them, so you should shoot them if you point the gun at them anyway...but that's a different discussion.) If you handle your SDVE series gun sufficiently, I think you'll find that the instances where the trigger actually gets unintentionally pulled hard enough to cock and release the striker and fire the weapon just don't happen in NORMAL use. I emphasize normal use, including taking normal safety precautions (keep your booger hook off the bang switch, use a good holster, etc.) The reason that you hear about "Glock leg" incidents is that the trigger on even a standard/stock Glock is much lighter than on a SDVE, and also most if not all of these incidents have a negligence factor. I've yet to read of any account where a human wasn't involved.
I'd suggest you carry your SDVE pistol unloaded for a while...to see how it works for you, and if you encounter any concerns. If you can't get comfortable with it, and you don't feel comfortable with an Israeli draw, then a different pistol might be a better choice...one with a safety.
There are people who advocate the "Israeli draw" method of carry to address just this concern. (That is, the pistol is carried without a round in the chamber, and the slide is racked as the pistol is drawn.) If you are going to use this method, I would suggest that you train extensively, until it becomes second nature, relying on muscle memory, and doesn't require you to "think" about your action. Even then, under stress, it may not go as smoothly as when you drill...but extensive drilling may help compensate for stress reactions, if you have done it to the point that it over-rides any other conditions.
However, as others have suggested, the SDVE pistols have a purpose-designed heavier trigger to alleviate two possible concerns: one being an accidental/negligent discharge; and the other being very similar, but involving firing unintentionally when you are holding on a person. (There are many that also say you should never point a gun at another person unless you intend to shoot them, so you should shoot them if you point the gun at them anyway...but that's a different discussion.) If you handle your SDVE series gun sufficiently, I think you'll find that the instances where the trigger actually gets unintentionally pulled hard enough to cock and release the striker and fire the weapon just don't happen in NORMAL use. I emphasize normal use, including taking normal safety precautions (keep your booger hook off the bang switch, use a good holster, etc.) The reason that you hear about "Glock leg" incidents is that the trigger on even a standard/stock Glock is much lighter than on a SDVE, and also most if not all of these incidents have a negligence factor. I've yet to read of any account where a human wasn't involved.

I'd suggest you carry your SDVE pistol unloaded for a while...to see how it works for you, and if you encounter any concerns. If you can't get comfortable with it, and you don't feel comfortable with an Israeli draw, then a different pistol might be a better choice...one with a safety.