mysql installer no packages found
No minimal installation is available from MySQL's site. They used to have an essentials version, but it's unavailable for versions >5.1.
One solution to your case is to create your own installation - it's not very complicated. The process (in general) is to include bin,data,lib, and share folders from a clean installation, run mysqld --install, and copy your my.ini file (you may need to tweak with its data folder). This can give sometimes you an installation size of about 5 MB.
Another solution will be to use MariaDB as a MySQL alternative - their MSI is about 80 MB.