I fail to see how using straps will effect core stability as the trunk is still unsupported and is able to freely move. Use core work to work the core and if additional grip work is needed add that in later. Having an ab exercise where your grip is the weak point just makes me think that you will be short changing the main purpose of the exercise- strengthening your abs.
Thats why I originally bought the straps. I wasnt strong enough to grip and perform the excercise as long as I liked, eventually switching to grip when strong enough. It just felt too comfortable when I used them.