To be sure all your questions are answered, I’ll try to take them in order. Removal of infected branches is recommended, but if you want to wait until spring and see if your tree is able to recover and contain the verticillium wilt that’s fine. The fungus lives in the ground and is not wind-borne.

Verticillium wilt will not leave your tree, but your maple may be able to contain it and recover if it has the right conditions. The fungus that causes the disease lives in the soil so keeping your shoes clean will help prevent spreading the fungus to other parts of your yard. Verticillium wilt spreads in weaker plants so keeping your tree healthy by following the suggestions below should help:

1. Be sure your tree gets at least an inch of water per week, especially during dry spells.
2. Fertilize the tree with a fertilizer that is low in nitrogen and high in potassium, but don’t fertilize too much.
3. Mulch around the tree. This will help prevent any damage to roots which may become an entry for the fungus and will help regulate soil moisture and temperature.
4. Because the fungus can survive in the soil for ten years, do not move the soil where it may contaminate another part of your yard, clean your shoes thoroughly when you walk around the tree. If you choose to remove your Japanese maple and plant another tree in that spot, be sure it is resistant to verticillium wilt, such as white oaks, elms, or poplars.

Third, there’s no rush to cut down the tree as it won’t affect the tree or surrounding area. You can remove the tree when you no longer believe it suits your purposes.

For more information, you may wish to read:

https://portal.ct.gov/-/media/CAES/DOCUMENTS/Publications/Fact_Sheets/Plant_Pathology_and_Ecology/VERTICILLIUMWILTOFTREESANDSHRUBS050808pdf.pdf

https://www.extension.iastate.edu/news/2005/jun/071602.htm

https://pnwhandbooks.org/plantdisease/host-disease/maple-acer-spp-verticillium-wilt