You should complete your applications at a later date. Check the processing time for the embassy that you will apply in (should be on their web page) and add a week or two to the estimated time.
As others have said, check with your immigration office... but if you stayed at an hotel in Chiang Mai, I'm pretty sure you need to make a new one, since the hotel would have done one when you stayed there and that voids your previous one, meaning that you are now registered as being in Chiang Mai in the Immigration system.
Just a tiny comment for your information (and to not confuse others)... You don't get a "60 days visa on arrival" - you enter without any visa (visa exemption) and get a stamp that allows you to stay for 60 days. Visa on arrival is a different thing...
there is another worry about overstays... If they end up in any interaction with the police during those 3-4 days, i.e. random police check or immigration raid, they risk getting arrested, detained at IDC, prosecuted and banned to enter Thailand for 5 years plus they will have to pay for the deportation flight (chosen by immigration).
I'm not sure what document you are referring to as most embassies have their own information...
For example, The Royal Thai Embassy in Stockholm don't have any checklists on their webpage (just a description on how to apply for visas through e-visa).
I never did it myself from Bangkok... However I have done border runs from other locations in Thailand and I recommend flying to Malaysia and go back on the next flight (unless you want to stay...).
I read the post and every comment and no where do I mention DTV (I am aware that it is a DTV group and that the OP asked a non DTV related question).
I tried to correct you. Yes he is coming as a tourist. Yes he will get an entry stamp that allow him to stay 60 days. No he will NOT enter on a tourist visa!!! That is what I am trying to tell you. He will be allowed to enter without any visa - visa exemption.
A tourist visa is something you apply and pay for BEFORE you travel (it is issued by a Thai embassy or consulate).