Paul
I would recommend against editing a copy of the raster to save the copy to disk. If you have (or can create) a polygon representing the county boundary, ArcGIS can use that to clip everything outside and consider it to be 'NoData' (transparent).
This is done by loading the images into a mosaic dataset (MD), then for each raster, loading the county boundary into the MD and defining the boundary polygon as the "footprint", then setting the MD property "Always clip rasters to footprints?" to Yes.
There's a slightly more elegant way to do this using "seamlines" rather than footprints to make it easier for a user to restore the map OUTSIDE the county polygon (e.g. if there is a legend or other info in the map collar they'd want to see).
If you've already done the editing, a faster (but not recommended) method may be to examine your edited tiffs and determine the pixel value outside the county pixels - probably either 0 or 255? - then you can define that pixel value as "NoData" and ArcGIS will make it transparent. If all are loaded into a mosaic dataset, the NoData pixels should not obscure underlying maps.
[NOTE: I edited this post to add this comment] One reason this is not recommended is: if your scanned maps have any of these NoData pixel values within the valid interior of the map, those pixels will also be transparent... The "clip to footprints" method is usually better but I'm just trying to be sensitive to time you may have already invested in making copies, editing them, then georeferencing them. But if you'll be doing more of this in the future, I'd strongly encourage you to follow our recommended workflow. You'll avoid duplication of data, degradation of quality with resampling, AND the transparent "noData" problem
Cody B
