You shouldn't have a problem (especially skipping rides - though I do encourage you to hit the GMR at some point in the day! it's family-friendly!), but just make sure you check the schedules and make a definate plan as to which order you will do them in. You can wait until you are at the park, but if you can grab the hours a few days before at the resort (the online hours can differ, always double check with the Disney-printed ones when you get on-site!) you'll be even better off.
Little Mermaid and the Muppets are continuous shows, so they shouldn't be a problem (though Mermaid doesn't open right at park opening) getting into whenever you can squeeze them in. FP Mermaid (since you won't be "wasting" a ride FP) for an extra time savings.
B&TB isn't a tough show to see, but the later in the day the performance is the more crowded it will be. The last show of the day is the most crowded. I'd try for the first one if you can, and your biggest scheduling hurdle will be out of the way.
Are you interested in the other shows? LMA? Indy? Millionaire? LMA is simmilar to B&TB as the ealier shows are better - but I'd FP this one if possible and get it out of the way as early in the day as you can. Indy has thinned out a bit since LMA, and isn't bad any time of day. Same for Millionaire - especially during slower seasons when you are going.
The only show I can't offer advice on is Playhouse, as I've never been; but by not doing rides it gets a whole lot easier to fit all the shows in. It's actually a very good idea - we are planning on devoting one morning/afternoon to shows-only this trip, just so we aren't rushing around so much trying to squeeze in rides at the risk of missing shows. We'll use another afternoon/evening for rides.
Have a magical time! I don't think you will have any problem with just a little bit of planning.
N.E.D.
