Converting SRTM hgt files from WGS84 to another CRS

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I'm trying to get slope data from the SRTM (Shuttle Radar Topography Mission) elevation dataset which provides many .hgt files. I've parsed the hgt files to get meters above sea level. When I'm calculating slope in degrees, my data tends to be quite noisy and seems a bit off.

Ex. the following slope maps (in degrees) are from a very flat area and mountainous area. The first one is really noisy and the second one seems uncalibrated.

Flat: https://i.stack.imgur.com/HGNJ8.png

Mountainous: https://i.stack.imgur.com/K02Td.png

I was told that this was because I'm calculating slope directly from the hgt files, which are in WGS84, and that I need to convert to a meter-based CRS before generating a slope map. I don't really know what CRS to use however, or how to convert between them.

I looked at some of the code on this website for the documentation for geopandas: https://geopandas.org/projections.html#re-projecting, and it seems like the re-projection example code could be helpful, but I don't know how to feed in hgt files to geopandas or convert between CRSs.

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