I am not sure how you plan on deploying the version you will develop locally and then publish to your website afterward.
I have never tried flywheel’s built-in deployment so that I cannot comment on.
What I do, I use WP Migrate DB Pro - usually, I only push the database changes from the local version to the live site, and then I manually upload the files via FTP.
However, not too long ago the plugin added a feature to also update plugin files and media library uploads. I tried a couple of times, but so far it is way faster for me to upload via FTP.
So, part of the process the plugin does is to change the URL in the database from your local URL to the live URL. You should not have to do anything. However, sometimes I have encountered problems where some URLs were not changed.
The plugin “Better Search Replace” is excellent in finding and replacing URLs in the database, also in serialized data if you need to fix URLs in the database after launch.
Regarding FTP - not sure what OS you are on, but here is my favorite: https://cleverplugins.com/fastest-ftp-client-macos/
I hope my rambling gave you a little useful feedback