I've made a 5e Paladin. I took Intimidate as a skill proficiency. Now that I am choosing my oath it doesn't really work with Intimidate. My DM is kind of a stickler so I am was wondering: are there any in-game means that I could use to change my proficiency to something else?
For a RAW stickler DM there is no way to change a proficiency.
A good DM should employ the power the rules give them to say "stuff the rules, go for it".
However, none of the paladin oaths are incompatible with an intimidating paladin. Paladins are deeply committed to the virtues and ideals of their oath: threatening to break the fingers of people who get in the way is perfectly compatible with their oath. In many ways it is better than the alternative: actually breaking the fingers of people who get in the way.
Rules Say No
There is no way, Rules as Written, to untrain a skill and learn a new one instead. Not magically nor mechanically.
But Talk to Your DM
It might be against the strict letter of the rules. I am a DM who tries to keep things as close to the rules as possible. I'd rather a player be invested enough to say, "this doesn't fit, can I change it?" and make them happy, than to disallow them a relatively tiny (at this stage) character change because the book says so.
You Could Not Use the Skill
If the skill no longer works with who the character has become, don't use the skill. That doesn't mean, he is able to unlearn what he already knows. I know it is a lost resource, but if you're interested in story over game, it is always an option.
Training A New Skill is RAW
There is a passage in the DMG about getting training as a reward (instead of a magic item), but it requires spending downtime to train skills and a willing trainer.
In exchange, the character is guaranteed to receive a special benefit. Possible training benefits include the following:
- The character gains inspiration daily at dawn for 1d4 + 6 days.
- The character gains proficiency in a skill.
- The character gains a feat.
But this, of course, does need your DM to agree, you find a trainer in the game, and spend sufficient time training to earn the skill.