Greasing bearings question

I am looking in the owner's manual for my axles (AL-KO) and a couple of things I'm unsure of. I planned on jacking up trailer to work on each wheel, but manual says it's not required (Ultrulube-equipped axles). Second thing is that it mentions using a grease gun (I was told to pack them by hand). Any thoughts, suggestions, opinions, gun options? Also, would any high temp grease be ok to use? I definitely need to work on them - a couple of the hubs are running warm.

Thank you much in advance.