Do i need to correct for family wise error when doing moderation and mediation?

Hi, I've been analyzing data for moderating and mediating relationships and am wondering how necessary it is to correct for family wise error in moderation and mediation analysis. I have read arguments for and against correction for family wise error in the literature. My moderation/mediation relationships are generally small, so my preference is not to correct, especially as I have controlled for relevant variables in the process. Most of the relationships found are consistent with expectations/prior research, although there are a handful that aren't and may be due to type I error, but may be a real relationship that needs further research.

Any thoughts or advice would be helpful.