If you have a coach, this is likely a decision to make between you. Ultimately, there's no right answer.
Course conditions will change Strokes Gained to a degree.
When entering your rounds with cored greens you can expect putting stats to be worse (and therefore Strokes Gained total). However, it wont impact Strokes Gained driving, and it will have a small impact on the approach and short game stats.
If it's only one round, the putting stats should average out with the trend so it won't have a massive influence on improvement opportunities.
If you're playing 5 rounds with cored greens then more likely to expect putting could be top 3 improvement opportunities, and so might be worth rethinking whether to add those rounds.