but problem is we cant get WSUS server access
Can you better describe what you mean by "get WSUS server access"? While it's not necessary to have physical access to the machine, it's an absolute requirement to have an administrative logon.
without having access to WSUS,is it possible to manage the installation of patches on windows server through Solarwinds Patch Manager
Well... Microsoft patches yes, because those can also be deployed via Windows Update; but for third-party patches, having administrative access to the server is quite necessary.