Shoes and layers

Whatever those shoes are, if they'll work in one place they'll work in the other. Shirts and pants jerked out of the closet will work fine too. You're making a big deal out of nothing. The rain coat idea is not so hot. Get a waterPROOF rain jacket that covers your butt instead. Your lower britches will dry out quickly enogh and they actually won't get much wetter than they would under a flapping raincoat. A jacket with a hood will keep you much more dry than one without,

As long as you have something more sturdy than a pair of flip flops, you will be fine in CT. It can be steep, and slippery if wet, for a few short stretches - but mostly it's a well traveled, wide trail. I haven't been to Murren, so can't give you good advice there. As Ed says. The ideal is a waterPROOF (make sure it says waterproof on the label), unlined jacket with a hood and long enough to make the drips go below your bottom. Zippered pockets and vents are also nice features. I pack clothes with an eye toward various levels of formality, normally a couple t-shirts for casual and a couple of button-up shirts for nicer restaurants. One or two warm items, normally a light sweater. If I need to, I layer one or two t-shirts under the button-up. If it's really cold the sweaters are added. The waterproof jacket becomes the top layer in wind, rain, or cold. If it's really cold, stop at a store and add some gloves and ski cap. I don't pack these unless I'm going in winter or the weather forecast is for very cold. Ideal pants are are suitable for casual Fridays at work, normally I prefer non-cotton (quick drying, wrinkle free) golf pants that look like khakis or a pair of non-cotton slacks. If I had access to laundry and was staying in one place, I might pack a decent pair of jeans - otherwise jeans are too heavy (and slow drying) for my pack list.

I would recommend a pair of Merrell shoes, I use the Geo-morph's and that is all I take when I go to Europe. Merrell's are the most comfortable shoes I have ever found and are very well made. As far as rain jacket I like the Marmot Mica, it's water proof and very light weight and packable. As for clothes, I like to do my own laundry every 3-4 day in my room so I buy shirts from Royal Robbins and Patagonia that are made from nylon/polyester because they dry quickly (3-5 hrs).
For underwear I recommend exofficio, they are simply the best because they are easy to wash, comfortable and last forever. I carry a large Go-tube of Woolite in my carry-on and could stay in Europe for a month easy with 5 shirts & 3 pairs of pants (also nylon/polyester). When I travel I find that the simpler you make your packing the more fun you have!

We did a trip like yours in late April (Lauterbrunnen, Lucerne, Cinque Terre). As most have noted, you'll need an unlined waterproof outer shell (not a rubber raincoat). Mine was from Columbia with a hood that rolled up nicely to keep in my Civita bag. I got too sweaty from a fleece jacket but one without sleeves was perfect for alpine weather, especially with the shell. All my shirts were easy-care long sleeves (roll 'em up for hiking in Cinque Terre). Pants were light weight hiking style (again from Columbia but available from several quality brands); blue jeans were okay (even Rick Steves wears them in his latest videos, but as he points out, jeans take way too long to dry); never felt I needed shorts. Shoes should be comfortable walkers; mine were Keens, my wife wore Merrells. Should have some tread and hard toe; no sandals and no real need for heavy hiking boots. Running shoes are miserable in the rain or snow. Be sure to wear blister-free socks or sock liners.