A lot of golfers like to use their putters around the greens. This is because there is less of a back swing and you can get a firmer connection with the ball.
The disadvantages of using your putter off the green is if you have a bad lie in the fringe or if you are more than a foot back from the green. Judging how hard to putt through rough can be a tricky skill.
A bump and run shot with a chipper is a good option for shots in and around the green. The chipper has enough loft to get the ball airborne slightly, avoiding the rest of the fringe and running onto the green.
I have seen Tiger Woods use his 3 wood around the green to achieve similar results. Slight loft to push through the rough and a long roll on the green. Rolling the ball is easier to control and is more predictable. Like a putt.
The Palm Springs 2EZ Chipper is similar in shape to a fairway wood. The new Wilson Prostaff HL Chipper is similar in shape to a blade putter.
When using your shipper take a narrow stance with your feet less than should width apart. Your weight should be distributed towards your front foot. Your ball should be positioned back in your stance, with the club leaning forward.
Swing the club like you are using your putter by using your shoulder and arms in a pendulum motion. Keep you hands ahead of the club head and let the chipper do the work.
The bump and run is a shot you can practice in your garden or even indoors with some airflow balls. It is not a pretty shot as there is not much loft but it is extremely effective.