My Mom died last month. She had been a JW for 40 years. I could not bury her in that faith as the family doesn't share the same death thoughts. All we said in the paper was that she was a deeply religious person. We buried her though our church. The JW'S have a talk at the hall so they are free to do that. The family thought about making her funeral private but thought we have nothing to fear. And funerals are for the living so we didn't want all those people telling us there scoop on death.
In your case, if you have a wake and then the funeral, why not give the wake service to the JW'S and have the funeral in your faith. You could say the funeral will be private and tell all family members where it will be. The JW'S can feed there brand of crap-o-la at the wake service. Just a thought.......take care and good luck. It is good to plan what you are going to do ahead of time, makes it easier.