I'm looking for a way to convert several TIFFs with Worldfiles to GeoTIFFs. Is there an option using ArcGIS or Python (Arcpy)? What is the best option you could recommend?
Have you tried ArcMap, Conversion Tools, Raster Toolset, Raster to other format? choose tif as the output. Also, I remember from ArcMap, table of contents, you can export an Image, tweak the settings. It seems ArcGIS prefers to create a Geotiff instead of tif/world file. Also with Geotiff you can assign a spatial reference.
I would recommend you to georeference the images with ArcGIS or QGIS in order to avoid distortions. If you save the outcome a world file will automatically produced next to the corrected TIFF image