It's a tough job!
Do you have a router?
I would mark the joint out in place using the female joint to trace around. If there is a radius edge the degree of difficulty increases the larger it is.
If you have enough to cut the end off and you can clamp it on and not have the clamps interfere with the router you have a template.
If not you can use the female side and clamp it on the waste side allowing for the thickness of the router bit, degree of difficulty is much higher this way.
Run a pattern bit in your router to trace the edge using your template, bonus difficulty if there is a radius edge to deal with, If your offcut has a radius you may be able to slice it off on a table saw or bandsaw so you have a thinner but flat piece to work with. If it is a full radius edge or bullnose there is a work around if needed.
Your not going to be able to route all the way through if it is a decent thickness top, so you should be into solid material i.e. past any radius so you ca adjust the cutter to have the bearing level with or above the grove you have made.
Carefully route out the waste material while being careful not to have the router tip, bonus difficulty if there is a radius edge to work with.
If it used connecting bolts depending on how much you have to cut off you may need to trim the bolts to fit or make a new recess for them or work around it.
Once you have done that swear never to do it again and have a sit down and a drink.
Jig is easier as long as it is the same type of jig, there are plenty of brands out there that may or not match each other.
