Reproject tfw without creating a new raster file

I have a quite big amount of georeferenced .tif with their .tfw in one folder. The orignal CRS is Gauss-Krueger, and now I want to reproject them to UTM.
My approach so far is to use gdalwarp:

"C:Program FilesQGIS 3.14bingdalwarp.exe" -s_srs EPSG:31467 -t_srs EPSG:3044 -multi -co TFW=TRUE -wo NUM_THREADS=ALL_CPUS "%mypath_import%!infile!" "%mypath_rasterUTM%!outfile!"

Ergo, I get a lot of new TIFFs and the process needs a lot of time. Is there a way to just reproject the .tfw into UTM coordinates? I think it’s quite a waste of processing power/disk space to create a whole new TIFF!