can I use IPV6 addresses instead of IPV4 for the NS1.mywebsite.com and NS2.mywebsite.com?
Today, the answer is sadly no. :(
Many recursive DNS resolver do not have IPv6 connectivity and cannot communicate with an IPv6-only name server.
Example: my ISP
My ISP (Free SAS/Proxad) provides direct IPv6 access for all almost subscribers (and the few other subscribers can have IPv6 if they know how to do 6to4rd). I have tested my ISP DNS recursive resolver, and they can access IPv6-only NS. But other clients of that same ISP (Free/Proxad) have done the exact same test, and the Free/Proxad DNS recursive resolver they are using (with the same IP address I am using) lacks this IPv6 connectivity.
Conclusion: even if you believe that your ISP handles IPv6 NS just fine because you have checked that yourself, you may be wrong.
Public DNS resolvers
I have tested some public DNS resolvers, and they cannot resolve on IPv6.
Do not confuse AAAA handling with IPv6-only NS
All these DNS resolvers have no problems with the handling of AAAA records.