Got it. There are a number of ways you could do it: for instance, if you’re not using ossia staves anywhere else you could give each of the string players an ossia stave (which will automatically be smaller), cue into that, then set the Layout Options in such a way that a) the ossia staves don’t show in the score and b) they’re not labelled “ossia”.
If all of the string players need the same bits of vocal material (or even if not, I guess), you could add a completely new player to the project (holding whatever instrument), then cue into that. Then assign that player to each of the part layouts, unassign it from the score layout, set Layout Options for the parts in order that they Hide Empty Staves throughout, overwrite the Layout names so they don’t refer to the extra player. Then if there are bits where some string players don’t need the cue staff, you could use Manual Staff Visibility to temporarily hide the cue staff.
Come to think of it, you could just assign the vocal player to all of the string part layouts, then (assuming you’re in 3.5 or later) use Manual Staff Visibility to hide the vocal player apart from where you need it. You’ll still need to overwrite the layout names so that they don’t say e.g. Violoncello & Tenor.