To ensure you plane to length and keep it square (while minimizing tear-out), you can try the following:
With a knife, scribe your finish line around the circumference of your board – both faces, both edges – transferring the knife line from your initial reference face as you go. You can then chamfer along the edges with a block plane – or whatever you have available – down to that line. Then plane the middle (the portion of end grain that remains “above” your line) until it is flat across the end grain face. I hope that makes sense… It’s the slickest way I’ve seen to plane a long piece of end grain without the fear of any tear-out – think I saw it on a Chris Schwartz video – maybe Paul Sellers – I can’t remember.
The suggestion to use mineral spirits works well, too. I prefer an oil-rag can instead of the wax on plane soles, however. I’ll post a topic on that since I received a question via my website about it.