Here is a link to the ifixit guide to repair the motherboard for the Kindle paperwhite. It is handy because it shows how to access the motherboard so that the USB port can be reached. It is visible in the image in Step.6 (the silver connector at the bottom of the board)
Kindle Paperwhite 1st Generation Motherboard Replacement
The USB is an SMD (surface Mounted Device) type USB connector. You will need the requisite tools and knowledge to remove/replace (or just re-solder) the connector.
Any reputable, professional mobile phone repair service should be able to do this for you. They should also give a guarantee for their work and of course are responsible for any damage incurred. Unless you take just the board and the part to them to get them to replace it. Just a thought. This may reduce the price of the repair
Here is a link to the replacement part for the Kindle. It is not a recommendation to use the seller. It is shown to give an idea of the price.