I agree, but think it's worth pointing out that it often does matter what acid you use.
The best example I can think of is dehydration of an alcohol to give an alkene. The counter ions (Chloride vs. sulfate) differ in their nucleophilicity and leaving group ability. HCl will likely give some substitution product rather than elimination. Also, sulfuric acid is a much better dehydrating agent than HCl...its reaction with water is much more exothermic, so this helps drive the reaction toward the alkene. In short, replacing H2SO4 with HCl would be a bad idea for such a reaction.
In your case, you're adding water to the molecule, so there should be plenty of water around and the acid's ability to dehydrate isn't important. As for chloride acting as a nucleophile, I'm sure it still does, but it doesn't lead to product. If chloride adds as a nucleophile, it will get kicked back out because it's the best leaving group. Even if it stayed (very doubtful), it would give an acid chloride that would hydrolyze much more easily than the nitrile. So, here it shouldn't matter which acid you use.