Before you start cutting and threading, you need to know the exact configuration of the system inside the boom. A typical internal outhaul system (you said "clew" connection, right?) has an internal cascade purchase set up.. the wire you see is NOT connected directly to the rope control line... you cannot splice then together... look at the pictures:
So.... if you can't find specs on your boat... which would include a diagram of the internal outhaul.. you at least need to take a look inside the boom. That would mean removing the end cap.. which I notice is fixed with pop rivets... drill those out and take a look. Also look for attachment points in the boom for the other parts of the cascade for clues. In my catalina 27 there is a forward static line, that when released allows you to pull the entire rig out... it is also used to adjust the position of the tackle inside. When you replace the end cap, instead of rivets, use self tapping screws with some Loctite.
That said.... if you are talking about the "topping lift" then the system may be much simpler and may even be one continuous line.... but is more likely a 2:1 purchase similar to pic one.