Assuming your areas of interest are rather small compared to the globe, you could set up a custom transverse mercator projection.
You have to know the geographic coordinates lat_0 and lon_0 of the origin of your CRS, and the direction of x and y axis:
+proj=tmerc +lat_0=51.4 +lon_0=7 +k=1 +x_0=0 +y_0=0 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
For use with Arcgis, the .prj file should contain:
PROJCS["Transverse_Mercator",GEOGCS["GCS_WGS_1984",DATUM["D_unknown",SPHEROID["WGS84",6378137,298.257223563]],PRIMEM["Greenwich",0],UNIT["Degree",0.017453292519943295]],PROJECTION["Transverse_Mercator"],PARAMETER["latitude_of_origin",51.4],PARAMETER["central_meridian",7],PARAMETER["scale_factor",1],PARAMETER["false_easting",0],PARAMETER["false_northing",0],UNIT["Meter",1]]
If they are not in parallel with North and East directions, a rotation would be necessary by using an oblique mercator projection:
+proj=omerc +lat_0=51.4 +lonc=7 +alpha=-10 +k=1 +x_0=0 +y_0=0 +gamma=0 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
The .prj file for this projection is:
PROJCS["Hotine_Oblique_Mercator_Azimuth_Center",GEOGCS["GCS_WGS_1984",DATUM["D_unknown",SPHEROID["WGS84",6378137,298.257223563]],PRIMEM["Greenwich",0],UNIT["Degree",0.017453292519943295]],PROJECTION["Hotine_Oblique_Mercator_Azimuth_Center"],PARAMETER["latitude_of_center",51.4],PARAMETER["longitude_of_center",7],PARAMETER["azimuth",-10],PARAMETER["scale_factor",1],PARAMETER["false_easting",0],PARAMETER["false_northing",0],UNIT["Meter",1]]
Here are both together (tmerc in blue, and omerc in red):
The lat_0 and lon_0 (or lonc) are the coordinates of your local CRS origin. You have to explore these with a GPS or from other maps. The angle you have to calculate from the coordinates of two known points on your local X-axis.
The only thing that does not work as expected is the millimeter as units. It should work, but does not in current QGIS :-(
http://hub.qgis.org/issues/9414
Update
Current QGIS versions are now able to work with local projections using mm as units.