You need a wad editor (my choice is Slade) and a map editor (my choice is Ultimate Doom Builder) to do that.
The first step is to change some lumps' file names.
The second step:
The next step is to replace the E1's sky with Sigil 2's sky:
I made a hacked executable (by using Doomkid's dehmake from his vanilla exe pack) to include Sigil 2's 9000 hp Spiderdemon and automap names, which is based on Doom-plus.
SIGIL2exe.zip (At least works fine on my side. But I'm not sure whether sharing hacked executable is allowed. If it is not allowed, I'll delete the link)
Playing Sigil 2 in DOS, however, is still not recommended. If you prefer vanilla doom's visual, Crispy Doom's latest build has native support for Sigil 2.