In my experience, the biggest hurdle when "cold contacting/emailing" a potential influencer is: TRUST. You might have a stand out product but they don't know you from Adam and in essence: you are asking them to do something. Most people don't do something because a stranger asked them to - and this is no different.

You have to remember: These influencers get pitched daily; someone always wanting something from them so human nature tells us -- defenses would be up. I would suggest not mentioning the affiliate program at all on first contact. Perhaps you first add value to them by: asking if you could write a non-product blog post for them. Or perhaps you ask them if they have the same pain point your product is solving and work with them to solve that pain point - with no strings attached. You have to prove to them you want to build a relationship - not get them to push or promote a product.

If trust is built and the time is right after that - you could ask them if they could share their honest (good and bad) pain point story to their audience (then, the affiliate program is just ancillary -"oh, and we track and compensate you via our affiliate program, for any sale you bring over as a result"). I'd also try to really make it clear that you want to work one-on-one with them to make it successful and as so you should offer them something you don't offer 95% of your other affiliates (discounts, giveaway to just their audience, etc.).

With this, you will build strong bonds, aligning your success with theirs - which makes for a good influencer/merchant relationship.

Good luck! If you have any questions - I am just a call away:)