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

#1
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.

Thanks
Lisa