What's your current height, weight, and general bodyfat?
Yes, scrap it and do any of these complexes 3 days a week. It'll take the tiniest effort to figure out any dumbbell alternatives needed.
The limited equipment is a big enough hurdle. Don't overlook push-up variations. T-push-ups can get some good upper back work:
Since you're also trying to keep the workout under 30 minutes, it's super-inefficient to try fitting in small stuff like four different arm exercises or chest flyes or specific rear delt work. Also, as was said, give the legs more attention and you'll see better overall results.