Yes cold calling does work and also cold emailing (although be careful not to come off spammy when cold emailing). Try to establish a connection before just emailing. Your best bet is to work your connections and their connections.
I know you said you do not have contacts in the target market, but maybe some of your friends, family, coworkers, etc.. do. How did you get interested in this market? Someone or something led you down the road this product so follow that road back to see who along the way can help you now.
Splurge on a premium LinkedIn account and hunt down contacts in the market. See where they are within your network and seek out introductions.
Once you land one or two clients use them to build out. HR and Legal are two very well connected groups of people and they tend to talk among themselves at various networking events and within their circles. Get references and use their connections.
Finally, you missed an opportunity here by not linking to your product/service. Even put it in your profile here. I know I would have looked at the site to see if (a) it was something that I could use, (b) if I knew someone that could help you, or (c) just to put on my radar if something popped up down the road.
Finally participate in forums, blogs, etc... to promote your product. Don't spam them, but become a resource in the market space. It may take some time to build a reputation but if people see you can be trusted as a resource they may just buy your product.