No, CiviCRM must be installed within one of these CMS platforms: Drupal, Wordpress, Joomla, or Backdrop. But this doesn't mean you need to use that CMS for your organization's main website — you can install CiviCRM (within one of those CMS platforms) on a subdomain.
The CMS handles the part of the application which deals with users (i.e. "reset my password" and other such functionality). The fact that CiviCRM delegates this functionality to the CMS does make it a tiny bit more complicated — but tremendously more flexible! For example, perhaps in 10 years your very small organization will have grown to the point where it wants a CMS which can integrate with its CRM. CiviCRM leaves that possibility open.
Suggestions for you
- Install CiviCRM with Wordpress (the simplest one)
- Or, if the installation process feels daunting, consider hiring a hosting provider to set up and maintain a CiviCRM installation for you
Instead of viewing the CMS as "massive overkill" I would encourage you to think of it as only one small piece of CiviCRM itself. It just happens to be a modular piece. The size and complexity of an empty CMS actually pales in comparison to the size and complexity of CiviCRM itself.