Could someone please suggest me, which files in my /boot partition would be safe to delete?
Don't "delete" anything. It's to do with old kernels - kernels aren't updated as such, new ones are just installed. So long as you don't need the old kernels, just remove the old kernel RPMs.
In fact there are a number of tools to help you. By default yum keeps 5 versions of old kernels (which is usually too many for the default /boot size - good joined-up thinking there!), that number is specified in /etc/yum.conf as "installonly_limit=5" - change that to a suitable number for you, personally I use '3', some people have '2' - don't put it at '1' because then you'll not be able to use an old version to boot in to in emergency.
The package yum-utils has the package-cleanup command to deal with various yum issues, including sorting out old kernels. Do
package-cleanup --oldkernels --count=3
to clean everything to do with old kernels leaving 3 versions on your system.
P.