Below is the barebones strategy, modify it based on your requirements including security, accessibility, storage and other aspects. There could be other approaches to achieve it, hence, evaluate the pros and cons of each approach judiciously -
1) You would need to attach a storage with Akamai like S3 or something similar.
2) Mount a dedicated path for the videos that would be served from Akamai instead of AEM-DAM. Say /videos/* would be served from your videos storage otherwise all the traffic would be redirected to your origin server which would follow the normal cycle of LB > Apache
> publish server farm. Any request that contains the mounted path /videos would not reach publish servers but get routed to Akamai > Storage space
3) For authoring/pushing the videos to storage space attached to Akamai, set up a script/jenkins job/SFTP job or similar that would be attached to a shared folder where super-users would dump the video files in this shared folder to be pushed to storage space. This shared folder may/may not be an exact mirror of your storage space. Depending on your requirements of full load vs incremental load, tweak this piece of implementation.
4) You would code absolute urls of videos in your video component (either prod or non-prod absolute urls, depending on how many workspaces/instances you have with Akamai for both prod/non-prod)
5) For flushing videos cache/maintenance, you would simply push the appropriate files to storage space.
Work with your IT team to evaluate the security risks/concerns around it based on your setup and with content authors to make sure that you would lose on AEM-DAM features like versioning, metadata etc.