One website suggests that existing rails could be used.

Obviosuly there are no rails from Catford to Forest Hill.
One interesting point on the map, which you can only see if you enlarge it, is that there is a new station which is apparently not on the DLR called Broadmead. This is positioned roughly where Bell Green is located.

I still have a suspicion that that is where the DLR team were planning to terminate the DLR, not at Forest Hill.

"One website suggests that existing rails could be used."

Catford to Forest Hill: via Crofton Park then Honor Oak Park perhaps?

The plans that I have seen indicate that the tracks from Lewisham to Catford Bridge will be used. I suugest the route might continue to Bell Green via Broadmead in Bellingham and possibly to Lower Sydenham.

How it will get to Forest Hill I have no idea!