Stirring might work, soxhlet wont work because when the aparatuss is filled then both ether and water would flow down. Also, since they are inmisscible you wont get any extraction. I used this contraption for similar problem:https://imgur.com/hxzBkV6
1) you put ether into flask,
2) put addition funnel on top of the flask,
3) close the stopcock
4) add aq. solution of your compound into the addition funnel so that the top is slightly bellow the side tube (you can layer it with ether optionaly)
5) connect with condenser (you need dimroth condenser for this where the cooling media flows insude the spiral) that has glass capilary tube connected to the bottom tip of the spiral, you need to have it connected in a way that the capilary has same heigh above the surface of solution otherwise you wont get any flow through it. (glass pasteour pipettes work best for this
Whats gonna happen is that the ether will condense in the condenser and flow through the capillary at the bottom of the aq. layer and then will rise up, extracting your compound. When the layer of ether is big enough, ether will overflow and fall down in the flask.