NASA has had simple approximations of orbital elements available on their website for years, however those only list the major planets and Pluto.
I needed approximate positions for big asteroids and dwarf planets for a project and couldn’t find them anywhere, so I calculated a linear best fit based on data from NASA Horizons.
The resulting data is available here: Keplerian Elements for Approximate Positions of Minor Planets
A quick note: Many trans-neptunian objects have orbital elements that move around all over the place. The approximations here are valid over the quoted time line (1950-2100) but you cannot extrapolate them into the future.