And you can't modify the machine.config file of course... What you can do is add a factory declaration to the app/web.config file, like so:
<system.data>
<DbProviderFactories>
<!-- The definitions below are examples. It's likely you have to adjust the version numbers to the version the dll you're using. -->
<!-- PostgreSql -->
<!--<add name="PostgreSql Client Data Provider" invariant="Npgsql" description=".Net Framework Data Provider for PostgreSql" type="Npgsql.NpgsqlFactory, Npgsql, Version=3.0.2.0, Culture=neutral, PublicKeyToken=5d8b90d52f46fda7"/>-->
</DbProviderFactories>
</system.data>
(this is for postgresql, but you get the idea). Then reference the dll in your project so it's included in the dll's in the app and can be found by .net's dll loaded (fusion) as it's not in the GAC. You might want to consult the documentation of Devart's mysqlconnect to be sure which dlls to distribute with your application.