Powershell: validate URL path, incorrect path vs non public path - powershell

Question

I am trying to validate a URL that, if valid, I will use to download a file. But I want to validate the domain and the full path BEFORE doing the download, so I can provide a meaningful error log.
Given paths like the following
www.validDomain.com/downloads/validDownload.zip
www.validDomain.com/downloads/invalidDownload.zip
www.invalidDomain.com/downloads/validDownload.zip
I want to be able to report
invalid path: /downloads/invalidDownload.zip
Invalid domain: www.validDomain.com
I can use
$uri = [System.Uri]$path
if (Resolve-DnsName -Name:$uri.host) {}
to test the domain. I can then use
if (Invoke-Webrequest $uri.OriginalString -DisableKeepAlive -UseBasicParsing -Method:head) {}
to test the full path without actually doing the download, but the only error I get is The remote server returned an error: (403) Forbidden., both when the path doesn't exist and when the path does exist but it isn't a publicly available path.
Is there any way, on the PowerShell side, to differentiate the permissions issue vs the incorrect path issue?
Or do I have no choice but to provide a wishy washy error in the log? I know effetely the path does not exist to the user who doesn't have permissions, I am just hoping there is some client side way to differentiate. But I may be running into the limitations of how the web has been implemented.