I bought a multiple voltage adapter from Maplins (it was on offer at £15), which has a recessed sliding switch for changing the voltage - so I shouldn't have to worry about accidentally frying the controller by using too many volts. The box says it supports up to 2.5A at 6V, which should be more than enough for this usage. It came with a set of eight standard adapters, with user configurable polarity - meaning they can be connected with the central pin positive or negative. If you connect the tip adapter the wrong way round, it would be like putting the batteries in back-to-front. i.e. bad. Having opened the motor control box, I knew I needed the central pin to be positive, and the collar to be negative.
When checking their website to add the link, I discovered that Maplins sell a £3 polarity checker, and it was in stock at the store I visited. That would have been quicker than opening the unit up to determine this - their sales guy missed a chance there, but otherwise was very helpful.
(I later found the polarity information in this review of the Skywatcher SK1309EQ2 by Robin Scagell.)
So far the mains adapter seems to work fine, although I did need an extension cable. During my first night of testing the power plug came loose from the control box a couple of times - maybe I haven't selected quite the right adapter? I should try with the provided battery pack as well for comparison.