I don't know how helpful I'll be considering I don't know much about these particular boots or grivel crampons but I'll give it a shot since no one else seems to be responding. If I were you, I most likely would buy a pair of hybrid crampons (rear welt, and front strap). I have no idea if Grivel offers that option but BD does in most general mountaineering crampons. You don't have to worry then about an automatic crampon slipping off due to the shoe flexing, but it will be faster than a purely strap on crampon.
My limited experience involves using Vasque Breeze boots (trail boots) with strap on BD Neve crampons, and using La Sportiva Makalu boots (mostly mountaineering boots) with automatic (pro) BD serac crampons. I haven't done anything crazy intense with either but I can't say I noticed much difference in stability. As long as both are fitted properly and tight, they perform about the same. The automatic ones are just faster to take on and off. They also won't loosen over time which is a little bit of a plus that you don't have to tighten the strap on the crampon like once or twice during a full day.
I would only use strap crampons with those boots. While the boots may have welts, they are not designed with crampon use in mind and you will likely run into issues trying to use a newmatic-style crampon.