"Grizzled veteran soldier who did his time in the Orcs Wars, and now just wants to run his tavern in peace", is represented differently in a game in which there is zero combat. You don't need anything mechanical at all to represent his Fighting ability - because it's not going to be coming up in the game. He will literally never be fighting anyone ever (that's what zero combat means). So how would you realise this character in a D&D game with no combat? Well, I would probably imagine he would be very intimidating, scars, from the war, a big build - let's say I'm not trying to optimise and put points in Strength and Con to represent that he's a big guy (because while abilities don't see a lot of use out of combat they do still mean something). But what we're left with is that the point at which this whole history of violence interacts with the game engine is through the Intimidate skill.
Step back from the mechanics and ask what you could do with a character like this in a pacifist game.
Our veteran might not fight any more - maybe explained by his having taken a vow of peace after some incident or other in the past, and renounced his Fighter skills - but he can tell war stories till the end of time, some of which might hold relevance to (or allegory of) the party's current situation.
He can look at someone for five minutes and size up whether that person could be trained to fight e.g. in an arena; and maybe also gain an idea of that person's level of courage.
He's seen (and probably served under) good commanders and bad ones, knows the difference between them and knows what made them good or bad. He's also served with good companions and bad, ditto.
He's probably travelled a fair bit of the realm via marching up and down across it and thus has more on-the-ground knowledge of the rural folk and how they think/operate than any pure city dweller (or noble!) ever would.
I could go on - and on, and on - but you get the idea, hm?
All you-as-player need to do is a) get your DM's permission then b) before play starts* make up this guy's service history - what units/legions/armies he was in; who his commanders/superiors were and a three-word note for each e.g. "stern, fair, aloof", "weak, indecisive, cheerful", etc.; what (if any) action he saw; where he went during his tour(s) of duty, and maybe anything else he might have done during his downtimes.
Then you can spend the whole campaign mining the hell out of all this for your war stories.
* - or very shortly after, once you-as-player have had a chance to look over whatever setting the DM's using.