I do that all the time, cut the size piece I will need, plus what I expect it to shrink, plus what I may lose in fraying despite having overlocked.
the only hitch in this: holes open up in the washer on some fabrics.
See what shrinkage you can get by the washing method ( your usual ) with a small enough piece. Then, perhaps run a different test with a fresh piece to compare: soak in hot 20 minutes, then dry in hot, maybe more than once. Aggitate, just don't add soap.
Between the recoverable stretch and the shrinkage you DID get ( on the no soap test ) , and leaving them a tad bigger, you may be covered for all the allowance you'd need.
This is far preferable than discovering ( having washed with soap ) that picks open up ( holes where threads are joined in weaving ) and be short, having dedicated the positions of cuts, and nothing is then repositionable.
The CRDaniels is good for just one thing, no holes, ever. All other COM, I never use soap unless I have tons extra.