Your meter is the regulator. It determines the hours of cheap rate (which if you have an Economy 10 meter installed will be the standard e10 times) and simply gives a reading: ‘peak’ and off-peak’ matching these.
Therefore, if you switch to economy 7 tariff on your economy 10 meter, you provide your readings and these simply translate to ‘day’ and ‘night’ for the e7 tariff. The only thing that happens when you change supplier, pretty much, is virtually nothing. Your electricity stays the same and you simply provide your meter readings to a new supplier, who make the relevant calculations and bill you accordingly (in a nutshell).
So, my guess, and it is a guess, is yes, I expect you could just complete the switch online without speaking to them. I would suggest calling them beforehand to ensure it is all ‘above board’ (although they have confirmed and provided this to me/neighbour already and told me to simply switch as if economy 7 previously). So, either way, if one method of switching proves unsuccessful you can always try the other (although this may be more time consuming). Should you wish to call them their contact number can be easily found by typing ‘scottish power phone number’ into google. I have never had problems verifying they are able to supply me through talking to customer service, as described above.
Good luck with your switch! I’ll be getting on with mine as soon as able to. Let us know how it goes.