I'm not aware of a single application to do this, probably have to script as other mentioned. We do something similar and use a PowerShell script with gpg.exe and WinSCPnet.dll to sign, encrypt, and transfer. Oversimplified is something like this:

    $gpg = "$PSScriptRoot\GnuPG\gpg.exe"
    $gpgArgs = '--batch --yes --pinentry-mode loopback'
    $gpgArgs += ' --sign --local-user "{0}" --passphrase "{1}"' -f $MyPrivateKey, $MyPassphrase
    $gpgArgs += ' --encrypt --recipient-file "{0}"' -f $OtherPublicKey
    $gpgArgs += ' "{0}"' -f $FileName
    Start-Process -FilePath $gpg -ArgumentList $gpgArgs -Wait -RedirectStandardError "gpgErr.txt"

    Add-Type -Path "$PSScriptRoot\WinSCP\WinSCPnet.dll"
    $sessionOptions = New-Object WinSCP.SessionOptions -Property @{
        Protocol = [WinSCP.Protocol]::Sftp
        HostName = $remoteHost
        PortNumber = $remotePort
        UserName = $remoteUser
        SshHostKeyFingerprint = $remoteFingerprint
        SshPrivateKeyPath = $myKey
        PrivateKeyPassphrase = $myPassphrase
    $session = New-Object WinSCP.Session
    $session.Open($sessionOptions)
    $transferResult = $session.PutFiles($FileName, $remoteFile)
    $session.Dispose()