There are keyboard commands to reorder tools in the "Tool Order" screen of Site Info (Ctrl + i and Ctrl + m on Mac). Unfortunately, there's no way to attain focus on a tool in order to accomplish this reordering via tabbing alone - the tab behavior only takes you to the "Cog" icon for each tool: https://www.screencast.com/t/dxTNd0N6
To be able to reorder via keyboard commands, you must first click on a tool in the list: https://www.screencast.com/t/xrTsouMq63k
Confirmed that this was also the behavior in the previous "Page Order" tool in 10.x: https://www.screencast.com/t/nxJVZ9lYQ8g
Ideally, the tab behavior would focus first on the tool itself (providing keyboard reordering capabilities), with the next tab taking you to the cog icon for the tool. The next tab would cycle you to focus on the next tool.