EDIT:
Your question is not very clear... You have already made the shapefiles? Arcpy can definitely be used to add a buffer to some existing points based upon a field value, is that all you want to do?
The answer below is assuming that you want to create the circle polygons on the remote computer...
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Your other option is to use GDAL/OGR, which is a free and open source GIS library that has Python bindings (things that let you manipulate it from Python). It would still have to be installed, but this is a lot smaller and easier to do than installing ArcGIS just to get Arcpy. GDAL/OGR works quite different to Arcpy, so there will be a learning curve, but it is still pretty easy to create polygons like you want.
The other thing you could try (75% certain it will not work) is provide the remote Python with a modified version of Desktop10.1.pth that points to the relevant folders that will have to be shared on a computer that has ArcGIS, this might allow the remote Python to import Arcpy...