If you're doing this manually anyway, you can download the full workbook, then select the sheet(s) you want to send, Copy them, then open a new blank workbook and paste them in. Save that as a .twbx and you're good to go.
If you want to do this on an automatic basis, I don't know of a way to accomplish this without some majorly ugly hacking. You could easily automate the export of the dashboards in question in the form of images or PDFs though (I know it's not the same as having the ability to interact, but it might be something)
In reading your question I'm not sure whether by dashboards you mean there are a) dashboards spread across multiple workbooks or b) multiple dashboards in a single workbook.
In the case of a) it's possible to control whether workbooks can be viewed, interacted with, edited, and downloaded at a workbook or project level for different sets of users or groups, you can see the Tableau manual on how to set that up.
For b) I don't know of any way within a single workbook to download some views (worksheets or dashboards or storypoints) but not others. However I do have an idea where you would set up two workbooks, one for interacting and one for download.
- The "interacting" workbook has all the views and interaction set up, download permissions turned *off*, and a URL action or an image object with a URL link to the "download" workbook that is of the form http://myTableauServer/workbooks/myWorkbook.twbx.
- The download workbook has only the views that you want to enable to be downloaded, and download permissions turned *on*. You might even be able to turn view permissions for this workbook off (so users wouldn't be seeing it in their list of workbooks) while leaving download permissions on, I haven't tested that out.
This would require some extra work on the construction end to make sure the views stayed in sync but would enable users to download only the data & views that they were allowed to.