if you're using a standard dynamically-compiled curl, then it's tricky because it will try to load the old libcurl from /usr/lib/x86_64-linux-gnu/libcurl.so.4
or something like that, but a statically compiled curl? you can just download it and put it wherever you want, it's standalone and static after all.
following the instructions from https://stackoverflow.com/a/56394968/1067003 with compiler flags "-s -Os" to tell the compiler to optimize for size, here is a statically compiled 64bit linux curl version 7.65.0 with httpS support via statically compiled openssl version 1.1.1c, which is xz-compressed and base64-encoded: https://pastebin.com/HhMYYQAS
use the following command to decompress it:
wget -O- 'https://pastebin.com/raw/HhMYYQAS' | base64 -d | xz -d > curl_static;chmod +x curl_static;
(i can't inline the base64 because it's too big for stackoverflow answers)