@cristian v. @Antonin H. You can update your 6.3 to a 32-bit version compatible with 6.5; there is not an installer itself for 6.5 32-bit but the process is connect to 6.5 server with 6.3 client and you receive the update packages to the client.
Indeed there is no support or workaround for 7.0 32-bit client.
You are correct, with 7.0, there is no more 32 bit client. However, if you put in your Dynatrace server URL in a web browser with port 8021, you can download the Webstart client with only needs Java to run. Also, with 7.0, the Dynatrace Web Dashboards are quite robust and can very possibly be a replacement for the non-administrators of the server.
@Harish P. Ramesh is not a Dynatrace employee. I would not download such binaries posted in a forum from a non-official location. Dynatrace will not be held responsible for anything that comes out of using such a link / file.
I am uploading the release files for AppMon and am wondering what this link contained, there was no 32bit windows installer ever released by us for 7.0 - we did not build it anymore!
As noted, the 32bit-client was desupported. I would highly recommend upgrading your infrastructure. This will be an issue with a lot of vendors.
On a side note, Oracle is de-supporting the webstart client also in future JREs.
Another option would be to move to Dynatrace - where you have everything web-based and don't need a client installer anymore..