Welcome to the forum, Carl.
Respelling up and down is actually two different keyboard shortcuts, but you can also set commands for filtering all sharp notes or all flat notes. Filter all sharp notes then respell them to the note name above (thus turning e.g. all G#s into Abs) or filter all flat notes then respell them to the note name below (e.g. turning all Dbs into C#s).
Cautionary key and time signatures work in a somewhat different way, in that Sibelius lacks Flows, which are Dorico’s containers for music. Flows are typically used for separating related or unrelated chunks of music: whether you’re dealing with movements in a symphony, hymns in a hymnal, technical exercises or whatever else, each song/hymn/movement/exercise is best handled as a separate Flow. Given the end of one flow is unrelated to the beginning of the next flow, cautionaries don’t appear at the end of flows. If there are situations where you need to change key or time signature, midflow, without showing cautionaries, there’s an easy workaround for that involving hidden Codas.