Are you talking about all Wowza files in the installation folder, or specifically about the videos in the /content folder? For the latter, it should be fine to upload them as ec2-user, as long as the user “wowza” as read-rights to these files, there’s no problem for Wowza to use the content.
User “ec2-user” doesn’t have any rights to the /content folder by default. But you can add that user to a Linux group and let the group own the content folder.
# create a new group
$ sudo groupadd wowzagroup
# add users to group
$ sudo usermod -a -G wowzagroup wowza
$ sudo usermod -a -G wowzagroup ec2-user
# set ownership of directory and its contents
$ sudo chown -R wowza:wowzagroup /usr/local/WowzaStreamingEngine/content
# set rights of directory and its contents
$ sudo find /usr/local/WowzaStreamingEngine/content -type f -print0|xargs -0 chmod 664
$ sudo find /usr/local/WowzaStreamingEngine/content -type d -print0|xargs -0 chmod 775