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External venting and ducting for existing rangehoood

Hello! I would like to have my existing kitchen rangehood externally vented. Currently it just blows up at the ceiling and there is no existing ducting. Unfortunately my kitchen is alongside a load bearing concrete wall. I assume that makes running a duct straight to the exterior a bit tricky. There's an existing 100mm duct a few meters away installed for a toilet under the stairs that I think could be used. I'm happy to review quotes for any options, although I'm part of a body corporate, so any changes to the exterior walls will need to be run by them. The house is a two story townhouse, part of a duplex. The exterior wall that the kitchen is alongside is made of concrete tilt slab with plaster coating. The windows are double glazed. The other two exterior walls of the house are wood with various claddings (imitation schist on one and fibrecrete on the other), but the kitchen is in the middle of the house compared to them. The first picture attached is of the current rangehood, the temptingly close wall to the right is the one with a 125mm concrete slab in the middle of it, that window there is double glazed and opens. A proposal I have though is to make use of the existing 100mm external ducting in the little toilet directly through the wall from the existing rangehood. The second picture is of that, where I've drawn the approximate location of the rangehood. That vent in the toilet vents externally as shown in the third picture. The external vent is a few hundred mm above the internal one (about level with the top of the cistern I think). That toilet is under stairs up to the first floor that run alongside the left side and up the back. So there is a low cavity behind those walls about the width of the stairs. It's difficult to get a good picture with the duct in the way but the fourth picture is looking mostly up from the vent in the toilet. It looks up between two studs the vent is attached to, shows the bottom of the stairs and the duct bending to head out the concrete wall. The fifth picture of the existing vent pulled out with the 100mm ducting exposed, for the record. I see the healthy homes standard says the kitchen extractor fan needs to be either 150mm or 50 litres per second. So I assume it's possible to get 50 liters per second from a 100mm duct? Assuming the fan can handle the smaller duct. Have have no idea what the make of the current rangehood is. It looks like it could be an earlier version of the robinhood "compact canopy" that Mitre10, but it doesn't have an branding. Just a sticker inside that says ST-NOVELLA-LINEA ST2KM2BP. If I need to get a new one for this project I'm okay with that, likely the current one has been in there since that place was built in 2004. Although it appears to be working well enough.