I have perpetual licenses for CS3,5 and 6, if I subscribe will that affect my perpetual licenses.
No. No effect at all. You will still be the proud owner of CS3, 5 and 6 and can still use them whenever you like.
While there may be some uses of CC, I would never store photos on a Cloud, and will
still want to use my standard software most of the time,
No need to store anything in the Cloud at all if you don't want to. I don't.
I store all my photos locally when using CC.
To reinforce what John has said, having Photoshop CC doesn't mean you have to work differently at all. You need not use cloud storage or even settings syncing, and you only occasionally need a network connection. The software runs on your local computer, just like the older versions, and just occasionally contacts Adobe (similar to your perpetually licensed software) to verify your subscription activation.
I have all the old versions installed, but I virtually never use them except for testing things while helping people out here on the forum.
You also don't miss what you have never had, but the converse of that is it would be a bad day if you had to give up on all the new features in CC. Just today, the gap between CS6 and CC got a little wider.