If you have decided to protect SharePoint document libraries through IRM management, you can prevent those documents from opening from the Browser as well. Here you can find the PowerShell settings to achieve the same.
$web = Get-SPWeb http://mylibrary/site
$list = $web.GetList("MyLibrary")
$list.IrmEnable = $true
$list.InformationRightsManagementSettings.DisableDocumentBrowserView = $true
$list.Update()
*MyLibrary is the SharePoint document library name.
*DisableDocumentBrowserView is the property name.