Accepting an answer is optional, and is dependent on whether or not the answer solved the askers problem. If it did not, the asker is not obligated to accept.
Additionally, you're worrying about a metric that really doesn't have much impact, if you think about where the majority of your reputation score comes from.
A really great, well-written and detailed answer is likely to get 4, 5, sometimes 10 upvotes. When you think about how 10 upvotes is +100 reputation, it sort of makes the accept score seem a bit negligible, being that it's a mere +15 reputation.
In short, stop focusing on getting users to click the green checkbox and instead focus on writing great content that the community will upvote. You'll find your reputation score, and the things that you can do on the site, increase much more using this strategy.
Moreover, when you focus on writing great answers, a side effect of this is that more of your answers will be organically accepted, without needing to be pushy or say anything to the asker. This frees you up to go and look for other questions to answer. :)