Government offices are closed on specified days during the Songkran (Thai New Year) festival. This year it was officially from the 12th-16th of April. Officials and other staff will be on holiday during those dates and you won't be able to get any official business done then. If your wedding doesn't fall on those dates (dates for the following year will depend on any 'replacement days' of holiday if the official Songkran day 13th April, falls on a weekend) then you should be able to get the officials to register your marriage.
Again, if your wedding isn't on one of the public holidays then transport should be as readily available as it normally is. If it does fall on one of the Songkran holidays then it might be tricky, but still possible I would imagine (at an extra cost, of course!).
If you are having the ceremony on one of the official holidays and it's not possible to get the marriage certificates done on the same day, you can wait till the offices are open again and get them done then. Getting a Thai marriage certificate is a slightly different process than it is in the UK. There is no kind of 'ceremony' attached to it, it's about as romantic as getting a TV licence. Many Thai people have their ceremonial wedding on a completely different day to the day they spend sitting in a the local office with a ticket number in their hand waiting for their details to be entered into the computer system and the marriage certificates to be printed out.
I'm not sure how the officials would even be able to do this outside of their office if they were to attend your ceremony.