According to the Oklahoma State Extension: "The fungus remains active on dead wood, producing numerous spores. Destroy diseased wood to reduce spore load in local areas. This lessens the likelihood that healthy trees near infested wood will become infected, however these trees may still become infected by wind-blown spores from other sources." Here is a link to their fact sheet on Hypoxylon: https://extension.okstate.edu/fact-sheets/biscogniauxia-canker-and-dieback-of-trees.html

The Missouri Dept of Conservation says: "Healthy trees are often already colonized by the Hypoxylon fungus, so removing infected trees may not protect nearby trees. However, in high traffic and residential areas, remove infected trees as soon as possible to avoid damage caused by falling limbs." Here is a link to their site with more info about Hypoxylon: https://mdc.mo.gov/trees-plants/diseases-pests/hypoxylon-canker

There is no recommended time of the year for removal. The sooner the better.