From my experience, yes, do it but you are right to be careful.
If you have just a few dedicated players, TALK TO THEM - setup a forum, a private chat, forum anything like this. give them VIP access, treat them as VIPs (cause they are :))
They will like meeting the developer of the game. Get to know them. People help friends.
Learn what it is that they want. In my experience, people are willing to do a lot for a benefit. We a F2P game and we've tried a number of things in the last 4 years, and almost always a carrot works the best.
I cannot tell you what that carrot is for your game and there are differences between players. For one person, simply a badge "Friend of the game" is enough. Gives them status, and they will work to get it.
For another person, it is a benefit in the game, perhaps money or some in game currency.
If you are asking players for a review, find a place in the game when they get the first high. Find a time/place in the game where they feel great, or when they feel the game is great. ask for a review then. Ideally, offer something for the review (see above - some carrot).
Give you an idea from experience:
In Realm of Empires, when a person captured their second town, they get a big high. Right then, we asked them for a review. We then got some conversion, say 20% of people writing reviews.
Later we tried to offer a carrot - we offered some free credits as a thank you / congratulations. Conversion doubled.
however, we still had a lot of 3/5 or 4/5 reviews. Not because people thought it was a 3 out of 5 game, but we naturally rate games this way.
then we added a added a "5 star reviews are most appreciated and help us grow! :)" at the end of the message, resulting in VAST majority of reviews 5 of out 5 now.
lessons learned : offer a carrot. tell them exactly what you want them to do.
another lesson, learned from different examples is to be direct - tell players directly what you want them to do. Do not make the message convoluted. the more direct the message, the better.
my 2c :)