Technically, you wouldn’t need a “paper” ticket since an SWR Touch smartcard could be used for the Weybridge to Wimbledon leg. If you set it up with their “Tap2Go” contactless solution you could touch in and out as if it were an Oyster card and wouldn’t need to queue for ticket machines (or offices).
The disadvantage of this is that, in order to change tickets at Wimbledon, you’d need to tap “out” of your SWR journey as well as tapping “in” to your Oyster/contactless journey. There are Oyster readers on the tube platforms at Wimbledon to do this (the yellow ones, not the pink ones) so you don’t need to go through the barriers, but having to tap two different cards, one after the other, every time you pass, rather than just the one may become a chore. A paper ticket may be easier – It’s your choice.