I can see two possible solutions to this problem:
Solution 1: Better Exposed Filters
Install the Better Exposed Filters module. There are over 31,227 sites using it at the moment. Don't let the fact that it is in alpha hold you back unless your organization has a policy preventing you from using alpha releases.
Solution 2: Custom Code
If you cannot use Better Exposed Filters for some reason, then write a hook_form_FORM_ID_alter() to modify your views exposed form the way you want.