It's currently not possible to customize the Log Email activity composer.
I found this feature request in our Ideas forum where other users are requesting a similar function. It's currently marked as "not planned", but I'd recommend supporting the Idea with an upvote and explaining your use case in the comments. Our product team uses that forum to collect ideas on how we can improve the product for our customers. Product pays particular attention to the top voted ideas & takes them into consideration along with other feedback channels.