Funnels are basically nothing more than aesthetics and don't do a great deal functionally apart from tidy things up and possibly direct some air flow.
What you see on the outside is 99% of the time simply a cladding that hides the uptakes. In steam days you would have the boiler exhaust going through it and in diesel plant set ups you may have engine exhausts, all as a seperate pipe inside the funnel. Many incorporate other items such as vents from tanks, crank cases etc, some include machinery space air exhausts and some will have steam plant relief valves venting to the top of the funnel.
In the case of the Envoy there would almost certainly be the boiler exhaust running up the centre as per your example but seeing as ventilation is via the cowls and there are external vents fitted there may well not be much else inside.
Some vessels were fitted with spark arresters on the top to help prevent sparks from giving a ships position away which consisted of basically a steel framework but a lot of them were removed after they had rotted away and started to fall apart.
If you are going to fit a steam plant and you run the boiler exhaust up the funnel or if you are going electric and you decide to fit a water vapour generator bot will provide a convincing internal flue. If not you could always insert a dummy tube to give the same effect. I would then airbrush the whole area, inside and out, matt black to give a nice sooty effect.