Assalam Alaykum Dear Brother,
Thank you for your question and for contacting Ask About Islam.
Maybe you have a misunderstanding about what public Shahada means. Let me explain.
You have observed Ramadan, attended Islamic courses, and went to the mosque regularly, which are all things that you have done in public, at least in front of the Muslims.
Taking the Shahada in public is not any different, you will have to stand in front of all the Muslims in the mosque and declare the testimony of faith. It does not have to be on Fridays when the mosque is full; it could be any other time, even if witnessed by few Muslims.
If you are not ready, it is not a problem. Take your time, you are already a Muslim. The public declaration is to solidify that stand.
The brothers and sisters in your community would like to celebrate your coming to Islam so they are anxious to hear you do so in front of all of them.
Simply explain your situation to the local Imam and tell him if you could do so in a more settled way.
Good luck and welcome to Islam!
I hope this helps answer your question.
Salam and please keep in touch.