I have an old cookie recipe which uses half crisco and half butter as the shortening.

It does make a difference. I have an English Toffee of my mother's that uses half butter and half crisco/margerine and I have used all butter, but the half/half works best.

Crisco also has a non-trans fat version now. I've also subbed coc oil for the crisco in recipes.

You could also try Spectrum for the shortening part.

I just made an old cookie recipe of my mother's, subbing butter for the Crisco. The all-butter cookies tasted great, but they were very thin and spread much farther than I had anticipated. I liked the flavor, but they were less cookie-like in appearance and texture.

Yes, but the substitution will probably have other effects, which may or may not be desireable. The cookies should be crisper, spread more, and brown sooner. Also, butter contains a significant amout of water (15 to 17 percent for most brands), whereas Crisco has none, so in using all butter you're also changing the amount of liquid in the dough; slight tweaks in the amounts of other liquid or flour might be needed.

Kenji Lopez-Alt has an interesting piece about tweaking chocolate chip cookie recipes that discusses some of the differences that butter makes versus other fats.

http://sweets.seriouseats.com/2013/12/the-food-lab-the-best-chocolate-chip-cookies.html