• 08.092 and it did not take him long to find a nice smooth egg-shaped one

Ah, the right tool for the job.  Nothing like it.

This word is, of course, attested in OED. I rather love one of the examples:

1854   J. H. Stocqueler Hand-bk. Brit. India (ed. 3) 370   Ceylon is egg-shaped.

“egg, n.” OED Online, Oxford University Press, June 2017, http://www.oed.com/view/Entry/59878. Accessed 13 September 2017.