There is no need to delete any of your WhatsApp messages or videos, but there is a good reason to save them, as you may want the info held on WhatsApp in the future.
Go into WhatsApp..
Click on settings..
Click on Chats..
Scroll right down and click on chat back up.
Do this just before you change to a new phone if you go down that route. Rightly so as Pasta says many older phones are no longer supported by Whatsapp. It is just a case of reinstalling it on your new phone and all your messages will be there.. Just as they were on your old phone.