AD7190 voltage reference
Just make the cables from your 4-wire load cell as short as possible and rewire from that point using 6-wire cabling to the AD7190: -

All that this adds to the error budget is the variable volt drop along the blue wires shown in my picture above. The shorter the blue wires are, the better the accuracy over temperature and the load cell maximum range.

Whether a precision reference is needed for my 4-wire load cell
application? If I use a precision reference, is my performance giong
to be better or worse?

It certainly won't hurt to use a precision reference but, a better method is to use current excitation.
You use a current source that produces the same approximate level of voltage excitation. This then keeps current flow through the blue wires constant so it's one less variable error to worry about AND, if your load-cell is not a full active bridge you will certainly get improved linearity when using a current source. See this table for the relative formulas: -

Table taken from this document. See also this document that makes linearity comparisons when exciting with constant voltage and constant current: -