i agree, swing away! (provided it doesn't become a prop, the fact that you are thinking about it before even using it means it probably won't!
FWIW, swinging is actually REALLY good for babies and children that can tolerate it, it provides vestibular (or movement) input to the brain in much the same way that providing little black and white cards or soothing music for babies provides visual and auditory stimuli. Movement intformation helps a baby figure out where they are in space, provided that they tolerate it well (you will know if they don't, i for example, STILL can't tolerate swinging, i get dizzy-as you can imagine i am a hoot at an amusement park!)
have fun!