Someone who is proud of himself, his moral values etc. however who is a coward in his general approach, related to anything in which he could get involved with, since he avoids most situations.
American English (not familiar with usage elsewhere in the world) tends to assume that someone who is proud and a coward will also brag a lot, talking about how great they are to make themselves sound better than the are. There is a connotation that these people are overly proud of themselves, and an implication that they are cowards, because only a coward would need to boast about skill/experience/bravery they don't have. So there is no word that means "Proud coward" but a lot of words or phrases that would give that meaning in context.
- braggadocious (adj from braggadocio)--boastful but hiding weakness
- Blusterer--someone who 'talks big' but never does anything
Common phrases include:
- he has a big ego but nothing to back it up
- she's full of false pride
- he's all talk
- she's nothing but hot air