You are in FL... You are really asking for trouble if you get a permit.
Having said that, it is also illegal for you to do it without a permit. You probably need a permit just to paint.
So what to do...what to do...kinda depends on how you intend to handle it.
The core purpose of the permit is to raise your taxes. Sucks, but true.
So, the question is, when, and how are you going to do it??
If you are going to take off 2 weeks and work on it during the work week- get a permit.
If you are unable to work clean enough that the exterior of the house looks undisturbed (including piles of debris) anytime during the work week when the inspectors are at work- get a permit.
If you are on questionable terms with your neighbors- get a permit.
If you live on a main intersection, or near any government employees or council members- get a permit.
If you can work weekends only, and keep it clean during the week, and think you will not get caught, avoid the permit.
If you get a permit in FL, I am pretty sure you will not be able to do your own work without a FL licensed contractor.
In most areas the penalty for getting caught without a permit is double the permit fee- not very expensive. YMMV in FL. FL is the most regulated state in the country for construction. (I am a licensed contractor near the border of FL, and own property in FL, but won't work in FL).