Much better to do it that way. Fist fights typically aren't a big deal to most cops unless one person goes seriously overboard. Pull a knife on someone, and you are looking (usually) at deadly force options for cops or civilians. Pull a knife up close and personal, and if the cops are called you have a much higher possibility of going to jail.
I've pulled a knife twice in confrontations. Once was a guy who had two large GSD. He was up on his roof and thought it was funny watching his dogs come after me. I pulled a Kukri out that I had on my side with the assumption that I was going to get bit pretty bad, but that I was going to kill the dogs (which I hate because I have always owned GSD). The guy no longer found it funny once the Kukri came out, and began frantically screaming at his dogs.
The second time was coming out of a lounge with my wife and another couple at night. We walked towards our vehicles, and I saw 5 or so guys who were at the front of an all night convenience store, 3 sitting and 2 standing. The two standing guys saw us, and must have figured us for an easy mark. They said something, and all of the guys sitting down turned and looked at us, then got up slowly and started to drift our way. We were about a half a block away, and I pulled my knife, and kept turning it back and forth the same way that you would use a signal mirror. They stopped, turned around, and went back to their previous positions by the store. I never would have used the knife for defense, if things had gotten to the level of fearing for our lives, I would have shot them.
On a side note, if you ever deal with homeless people, the majority of them keep flathead screwdrivers on their person for defense. A sharpened flathead screwdriver is a wicked thing to get slashed or stabbed with, especially if you see what the tips usually look like. The reason they use a screwdriver instead of a knife is that a knife is more valuable and cops are more apt to hassle them for illegal weapons. A screwdriver is a just a tool....
That little revolver you just got is a great weapon, make sure you get a good holster for it.