If you want to distribute manually your .snap packages, then you can certainly do so.
For example, the libreoffice snap is easily available for download at https://uappexplorer.com/snap/ubuntu/libreoffice The recipe to create the snap package is shown on the same page. You can recreate the snap package and then keep it for yourself. Or, upload it to your website and share with your friends.
After you download the .snap package, just click on it and it will prompt you to install it.
What you do not get with snaps, is the source code of the Ubuntu Store. Most likely, if someone is really interested to replicate the store, I believe it is easy to reverse-engineer, then create a reference implementation.