How do I factor sweep and dihedral in the lift equation?
Snorri Gudmundsson's "General Aviation Aircraft Design"'s equation 9-57 allows you to estimate the lift coefficient curve's linear slope for trapezoidal/swept wings:


Note: the equation is in radians, not degrees

As for the dihedral, Equation 9-33 estimates the impact on angle of attack and Equation 9-35 estimates the resulting lift force:





Let me know if it's not what you wanted, though, I didn't quite get the "without factoring it into the lift coefficient." part - isn't the question's title about how it impacts the lift coefficient?