The first use is unknown to me - an archaic slang term perhaps?*
The second use is a common British phrase, and not rude. One's pecker is one's nose. Equivalent to 'keep your chin up'.
If you are doing a general conversion from British to American (spelling, common words, etc) then it would be reasonable to change both instances. But if you are otherwise leaving the usage of (say) colour, tap, pavement, vest, etc., then I'd leave these too. You should add a 'Notes on the text' section, to either explain the change, or to note the meaning of the phrase if you leave it.
*Just found
a reference: it is indeed an old slang term for appetite, from the work 'peck' in the meaning quantity (of food).