Running and hypermobility?

Options
Ok so I've been psyching myself up to do c25k once I finish 30ds and have been all excited to start, but I've just had a flashback to my physio years ago telling me to avoid high impact sports as I've got hypermobile joints, my ankles and knees being worst affected!

At the time I wasn't doing any exercise, and was in pretty bad shape, but she gave me a load of exercises to do to try and build up the muscles to support them, which I've completely forgotten lol!

Anyway, would it be really stupid of me to attempt c25k, or if I took things slow would it be ok? And is there anything I can do to build up the strength in the joints, or would generally being more active be enough?!