Thanks for the reply Marco.
I would normally use my laptop and that way I can get a wired connection, which may mean that Skype runs in a higher bandwidth mode (?)
The USB mic doesn't cut the weight down enough to be worthwhile. I found a Rode Smartlav+ which weighs nothing - it is advertised for iOS but presumably works with laptops too. Also, it seems that "with the smartlav+ the user simply mounts the microphone on the talent, connects it to a smartphone or tablet headset jack and records via the rode rec app for ios, or any other audio app of their choice". So if I buy that one, I get to be "the talent". Sold... or nearly - I'm just not sure whether it would be noticeably better than the internal mic / mic array.