Your instincts about this are great! Google Ads and a dummy web site is a great way to test your idea, as is talking to potential customers. Most people don't do either of these.
At Blue Fish, we use cold calling both for sales and for market research. When doing research, I've used two approaches, depending on what I'm trying to learn.
The first approach is a "offer something of value" approach. It is to make what is essentially a sales call, and instead of offering a product, I offer a report. The most recent example of this is when I wanted to understand what my potential customers were planning for the upcoming year (with respect to a third party product with which we integrate). I offered them a "benchmark report" where they could learn about what other companies in their industry were planning to do with that product (were they planning to upgrade, increase/decrease usage, switch to a competitor, etc.). They could purchase the report for $2500 or get a complimentary copy by participating in the study. Some are not interested, but others are excited about a free way to get a $2500 report that can help them validate their decisions. If they say yes, I schedule an interview during which I ask them questions that I will need to write the report as well as questions that I have for my own market research purposes. This approach has a nice side benefit that it reinforces the perception that I am an expert in my field.
The second approach I have used is the "flatter, then beg for help" approach. I've called people that I hardly know as well as some that I don't know at all. I try to find someone that is himself/herself an entrepreneur and might remember what it's like in my shoes. I tell them that I have been following their career, read their articles/books, paid to see them speak at conferences, etc. I really respect their ideas, and now I'm wrestling with a question, and could I take 15 minutes of their time to help me out. If I do this well, I can often get them to talk to me for an hour. I've done this via email as well, which I find gets me slightly better results than cold calling (with a lot less rejection).
If you decide to make cold calls, there are two major hurdles you'll need to get over. First, just getting the person you are trying to talk to on the phone. Since you are trying to call attorneys, you'll almost certainly get their receptionist or secretary (we call them gatekeepers). Their job is to make sure nobody gets to talk to their boss unless their boss is expecting the call. The other big hurdle is that you have to avoid setting off the "Sales Call Radar". We can all tell a sales call within 5 seconds of answering the phone, and you have to disguise your call so that it doesn't seem like a sales call.
Here's what I recommend:
Let's say you are calling for John Smith. When you call the main number, don't ask for John Smith, ask instead to speak to John Smith's secretary. When you get her, say something like this. "I'm looking for an attorney to help me out with a project, and I thought of John. He's probably not interested in it, but would it make sense for me to describe it to you, and maybe you could tell me if you think it would be something John would want to talk to me about?" (It's important that she feel like she's in control of the call, which is why you ask her for permission before you start telling her your proposal.) She will say yes, and then you follow with something like, "I'm thinking of starting my own business, and I need some help. I have an idea for a product that might be useful to a law firm. I know John knows a lot about running a law firm, and I thought he would be the perfect person to tell me if my idea holds water or not. I don't suppose he'd be willing to talk to me for 15 minutes - I mean, is John even the kind of person that would have coffee with someone like me, even though there's probably nothing in it for him?"
Your goal here is to turn the secretary into your champion. She doesn't want to feel like she's working for a jerk, so she'll probably say "Yes, John would do that if he had time, but he's very busy." Tell her that you're in no rush, and you'd be happy to meet even a few months from now. Now, there's no reason for her not to schedule the appointment, or at least transfer you to John so you can ask him yourself. And the best part is that in order to keep from looking foolish, she will sell it to her boss, telling him it's a good idea for his reputation or whatever.
There's one last thing to do in order to secure the appointment. You'll want to minimize the chance that John will cancel the appointment. Here's how you do that. After you get a day/time agreed, say something like, "OK, Next Thursday at 1:00 - that sounds great. Now, I know John's very busy, and he probably gets called into court all the time. Is there any chance he'll have to cancel this appointment?" If she says Yes, then say "Is there a day that would work better for him? Maybe a day of the week where he doesn't go to court or something?" You're trying to preempt any reason for him to back out.
Then, of course, all that's left is to be your charming self when you meet John for coffee.