If you use plain C and only the part of the Win32 API that has been availlable since 95 that should be doable. No modern toolkit/SDK will likely enable you to do that. The problem will be finding downloads/sources for OS, SDK, and IDE old enough to target Windows 95. You might be able to use DirectX 8, but it will require installing DirectX 9 on newer versions of Windows as a dependency (DX10+ is not backwards compatible with DX8 and DX8 is the latest you get for Windows 95, DX9 is still availlable for Windows 11). Your game will have to be offline only or rely on insecure network stack because hardware old enough to run 95 does not have CPU instruction sets required by implementations for modern SSL.
would this greatly affect the development process at all?
Well, take the information I provided and have a guess ;-)