In Scan Mode, setup violations will not a issue, but hold violations should be taken care of. For violations occured at SIN port of flops, so just add delay cells before SIN. In Shift Mode, setup violations also not a big issue, but when fixing hold violations, we should take care of those violations related to data input of Flops. If add delay cells before D, may induce setup violations in normal function mode.
And we can also ajust clock tree to fix hold violations.
Generally, scan paths only need to be taken care of after post-routing.