Bear in mind that in the UK in general dive charters dont operate as they do in the US. There wont be a DM employed by the boat leading a group of divers. If you book on a boat yourself youll have to sort yourself out with a buddy or dive alone (if the skipper permits solo diving).
Diving from a UK charter is your own responsibility; no-one is going to query whether youre using tables or a computer or how you use them. Ive never been asked to show my qualifications on a UK dive boat. Generally you fill out a Next of Kin details form, so they know who to contact in an emergency and give a note of your expected dive time, so they know if youre overdue. Dive boats are almost invariably operated as live boats (if wreck diving a descent line will deployed) and either have a lift or a dive ladder, in either case you get back onto the boat fully kitted (no taking fins off to climb a ladder). Dont worry about this, Skippers are always very good at bringing the boat alongside you. Diving from a RIB you will remove all your kit except fins and pass it up before finning/hauling back aboard. Deployment of a dsmb from around 6 metres is pretty much expected nowadays unless you come back up the descent line.
If you want to go on an organized trip with a DM to lead you round then youll need to book through a shop onto one of their scheduled trips (or they might arrange one just for you, especially if you just want to shore dive). A trip like this will look at your qualifications and be much more active in looking after you but computer diving is pretty much standard here.
I suggest contacting Edinburgh Diving Centre theyll be able to hire you cylinders etc. and put you on one of their trips or arrange one for you.
Edinburgh Diving Centre
Alternatively, log on to Finstrokes and ask on the forum if anyone is diving when/where you want to dive:
Finstrokes
Youll probably find someone wholl help you, possibly lend you a cylinder etc. and the dive guide map is extremely useful in deciding where youd like to go.
On the east coast the water temperatures are a little bit cooler but generally there is slightly better visibility. However, the east coast is much more exposed and weather dependent. The west coast sea lochs (Loch Long and Loch Fyne) are an easy drive though and you will be able to dive there regardless of the weather. Water temperature is slightly higher but visibility generally poorer in the west.
Driving to Oban from Edinburgh and back is possible in a long day and Puffin Dive Centre do offer a shuttle RIB service and you can hire a dive guide. Its not cheap and theyre not my taste but they might suit you;
Puffin Dive Centre - Scuba Diving, Commercial Diver Training
Edinburgh to Scapa and back in a day just wouldnt be possible. Its a five hour drive to the ferry ports. However, if you had a weekend then it is a practical proposition. Scapa Scuba would be your best bet as an individual diver rather than the usual group of 12 chartering one of the boats.
Dive Scapa Flow Orkneys - Scapa Scuba