The challenge will be removing the DRM from your Kindle books. You may need to Google around a bit, but here's a high-level of what you need to do:
1) Seek out a tool called "DeDRM". The original plugin is no longer supported, so you may want to search on GitHub for the fork from NoDRM, which is still maintained.
2) Download Calibre if you don't already have it and install the DeDRM plugin.
3) You now need to get your books from Amazon into a format that DeDRM is able to crack. One method is to download the Kindle for PC app, but this method can be finnicky because Amazon keeps changing the DRM schema to avoid being cracked and you may have to track down an older version of the install. The easier method is to pull the books off your Paperwhite itself. So inside of Calibre, configure the DeDRM tool and enter in your Paperwhite's serial number (this is needed because the serial number is used as part of the encryption).
4) Finally, try importing one of your Kindle Paperwhite books into Calibre, and try opening the book using Calibre's ebook viewer. If you can read the book (i.e. the text is not scrambled), the decryption was successful. You can then load the rest of your collection. You should now have a collection of DRM-free AZWs.
5) The final step to getting the books over to your Kobo is converting them to a compatible format. Calibre has a built-in conversion tool for AZW to EPUB, however some people complain that the built-in tool can mess with the formatting. You may wish to download an additional plugin called KindleUnpack, which will produce an EPUB or MOBI file that is closer to the source material.
You can try all of this before getting a Kobo to make sure that it works. I've set this up for various family members who all uses Kindle exclusively, primarily so that we can share books with each other, but also just to make sure that everyone has a good backup of their collection.
1) Seek out a tool called "DeDRM". The original plugin is no longer supported, so you may want to search on GitHub for the fork from NoDRM, which is still maintained.
2) Download Calibre if you don't already have it and install the DeDRM plugin.
3) You now need to get your books from Amazon into a format that DeDRM is able to crack. One method is to download the Kindle for PC app, but this method can be finnicky because Amazon keeps changing the DRM schema to avoid being cracked and you may have to track down an older version of the install. The easier method is to pull the books off your Paperwhite itself. So inside of Calibre, configure the DeDRM tool and enter in your Paperwhite's serial number (this is needed because the serial number is used as part of the encryption).
4) Finally, try importing one of your Kindle Paperwhite books into Calibre, and try opening the book using Calibre's ebook viewer. If you can read the book (i.e. the text is not scrambled), the decryption was successful. You can then load the rest of your collection. You should now have a collection of DRM-free AZWs.
5) The final step to getting the books over to your Kobo is converting them to a compatible format. Calibre has a built-in conversion tool for AZW to EPUB, however some people complain that the built-in tool can mess with the formatting. You may wish to download an additional plugin called KindleUnpack, which will produce an EPUB or MOBI file that is closer to the source material.
You can try all of this before getting a Kobo to make sure that it works. I've set this up for various family members who all uses Kindle exclusively, primarily so that we can share books with each other, but also just to make sure that everyone has a good backup of their collection.