I had the bonnet cable snap on my 156; not exactly the same as the 147 but similar.
The cable runs from bonnet pull to N/S wing. along the wing to bulkhead, along the bulkhead to O/S and through the bulkhead. The cable consists of an outer and inner (Bowden style), with nipple at bonnet end and barrel at pull end.
Routing a new cable looked to be a nightmare so I purchased some cable inner, a barrel and a suitable nipple. Pulled the old inner all the way out and used it to de-rust the inside of the outer by pushing it in and out of the bonnet end while dribbling 3-in-one on the cable inner.
Then I soldered the barrel on one end and pushed the new inner through from the pull end and clipped the barrel back in to the pull lever. As long as you have cleanly cut and tinned the other end, it should push through the cable outer without problems.
At the bonnet end, trim the inner cable to length and solder on the nipple. This is easiest done with plumbers solder melted in a small container, coat the cable end with plumbers flux and dip into the melted solder. I did it this way because heating the cable directly with a torch it is too difficult to get the correct temperature; too hot damages the cable; too cool and the solder won't flow.
I expect the 147 cable is similar length to the 156 at 2.8 metres. That's a lot longer than the average bicycle cable; I bought a 30m roll of 1.5mm cable, but you can get 3m cable inners for tandems.