Shimano's Interactive Glide chains are slightly narrower (by 0.2mm, e.g. see
here) compared to their HG/UG chains (i.e. 0.1mm each side), and it is of the same width as most SRAM/KMC 7/8 speed chains.
I very much doubt that you will encounter any problem - chainsets are rarely chain width sensitive, the reason is because a chain's inner width is quite a bit wider than the tooth of a chain ring - so chain rings have to be far apart enough to ensure the chains don't rub on the adjacent rings, especially given the gap also has to accommodate changes in chain line in different gears at the back. Because of that, a mere 0.1mm difference in outer width on each side of the chain has to be of little if any consequence.
Actually a more common concern is in using a modern narrow chain with an old chainset (in case the narrow chain falls in between the chain rings) - I use a 9 speed chain on an early '80 5/6 speed chainset, and have never had any problem whatsoever.
Sheldon's useful comments related to this topic is
here.