Hi Rich,
Unfortunately Microsoft Azure RemoteApp requires a Mac OS of 10.9 or later, if you are worried about the day to day performance of your other apps, you could try a dual boot setup - Either set a partition on your hard drive, or use a separate external drive (or usb stick) and install the newer OS to this, on boot-up you would then have the option of which operating system to use – Your existing one, with your existing apps, or your newer one with RemoteApp. This would also allow you to test the performance of your hardware with the newer version OS.
Please Note; this is just advice, before proceeding I would recommend performing a full backup of your system, also you may want to consult an Apple expert prior to commencing.
Kind Regards,
Si