Low ohms shunts are often made form a alloy called Manganin. Due to the alloying elements it has a considerably higher resistance than pure copper.
Pure copper does not work well for a 2 nd reason: the resistance changes quite a lot with temperature (some 3500 ppm/K), the special resistor alloys have a much more stable resistance (often < 100 ppm/K, good ones < 10 ppm/K).
For a DIY replacement one could use stainless steel - it has a relatively low TC. However soldering is not easy and needs special flux. Brass is also considerably better than copper, but the TC is not as low as with stainless.