Nemo is more a part of the Cinnamon desktop environment than any given distro (if you use say XFCE Linux Mint it will instead be Thunar).
Also the save dialogue probably depends upon the program being used, or at least the underlying toolkit it is built against (GTK being popular but there are several others
https://wiki.wxwidgets.org/WxWidgets_Compared_To_Other_Toolkits ).
Afraid I don't know what, if any, options might be available for the various toolkits. Looking at GTK's manuals, which is probably what most programs you use are based upon,
https://developer.gnome.org/gtk3/stable/GtkFileChooserDialog.html then even if you compiled it you seem somewhat limited in options.