Like the posting above mine the attitude of shops varies from place to place. The thing in your favor right now is the season. Many shops, particularly in colder regions, are struggling to get through these winter months and will most likely not be swamped and otherwise welcome the work. To cut down on labor cost, the stuff that requires special tools is as follows:
Bottom Bracket-removal and installation tools are specific to type of bottom bracket
Crank set - if your current crank set and bottom bracket is a square hole/square taper then you will need a special tool for removal, to reinstall you only need a 14mm socket and ratchet wrench. The new Ultegra crank set should be even easier to install without any fancy tools.
Chain- requires a special tool to push the pins out and into place
Cassette- requires a special tool to remove the lockring holding the cassette on the freehub body, plus a chainwhip to grip the cassette to keep the freehub body from turning while removing the lockring.
Cables and housing- it is best to cut housing and cables with a tool designed for the job (though a dremel tool with a cutoff wheel works suberb as well)
For ultegra the tools you will use most often to install and setup components are a 5mm allen wrench, a needle nose pliers (or any kind of pliers to pull on cables with), and a phillips head screw driver (to adjust hi-low limit screws on derailleurs). None of the ultegra parts on my wife's bike use a an allen key larger than 5mm and the only thing I can see that needs anything smaller would be the derailleur pulleys and the small adjusting screw on the side of the brake calipers which both take a 3mm allen wrench. The only thing on her bike that needed anything larger than a 5mm allen wrench were the crank bolts on her square hole dura-ace crank arms that needed an 8mm allen wrench. Pedals most often use a 15mm open end wrench but a an adjustable wrench will do in a pinch. So for very little investment in tools you can do most of the install work yourself.
I recommend picking up a copy of Bicycling Magazine's complete guide to bicycle repair. I got started repairing my ride back in 1986 with a copy of this book after watching the mechanic at the shop I bought my bike from adjust my brake by sidekicking my bike (no ****). I have built up many a bike with the knowledge I learned in that book years ago, and refined that knowledge with trial and error. With a good book and all the information on this forum and other webpages at your disposal you should be able to set your bike up just fine.
When I started working on my bikes I was scared to break open my hubs, headset, and bottom bracket...but after the first time doing an overhaul following the guide book step by step that fear quickly went away. The only time I go to a shop for work done is to have a headtube or bottom bracket faced as these jobs require a very expensive specialized tool to be done right and since it usually only needs to be done once in the lifetime of a frame it is hard to justify the cost of the tool for a home workshop.
I don't know where you are located but if you are near RI, you can bring your bike by and I will be happy to walk you through the installation of your parts. My wife is very happy with the Ultegra/dura-ace bike I built her a couple of years ago.
-J