[RPG] Can a person make a magical pact for something other than warlock abilities

The printed rules leave room for interpretation so your DM must rule it

You can use your action to create a pact weapon in your empty hand. You can choose the form that this melee weapon takes each time you create it (...) This weapon counts as magical for the purpose of overcoming resistance and immunity to damage. (PHB 107)

You can transform one magic weapon into your pact weapon by performing a special ritual while you hold the weapon. (...) You can then dismiss the weapon, shunting it to an extradimensional space, and it appears whenever you create your pact weapon thereafter. (PHB 108)

What the rules don't say is whether the transformed magic weapon holds its form or can also take a form chosen by the Warlock, and I can read the rules-as-written both ways.

• The first paragraph refers to an otherwise nonexistent weapon, which can be shaped, whereas the second refers to an existent weapon which should keep its form, hence "it appears", "it" the weapon.

• The first paragraph describes what happens to any weapon, nonexistent or existent which the Warlock summons, hence "it appears whenever you create", and "create" assumes "you can choose the form".

I don't think you can apply "specific beats general" here as there is no necessary contradiction between the specific and general rule.

I suppose the main idea of the second part of the rule is to allow you to have magical weapons that do extra cool stuff, and sometimes that might be tied to the specific form (for example, a Trident of Fish Command). But in any case, as is (for some frustratingly, for others liberatingly) frequent in D&D 5e your DM needs to rule this one.

Official ruling

If your table puts stock in official rulings, then the answer to this question is "you cannot change the form" (as pointed out in @DerekStucki's answer):

Once the bond is formed, the magic weapon appears whenever you call your pact weapon to you, and the intent is that you can’t change the magic weapon’s form when it appears. For example, if you bond with a flame tongue (longsword) and send the weapon to the feature’s extradimensional space, the weapon comes back as a longsword when you summon it. You don’t get to turn it into a club. Similarly, if you bond with a dagger of venom, you can’t summon it as a maul; it’s always a dagger. (Sage Advice Compendium, v1.14, p. 5)

Your problem isn't that you need to persuade your GM to change how the Warlock class works. Your problem is that you've fallen prey to what I'm going to start calling "the Nomenclature Bugbear."

Each character class is a collection of abilities built around a concept frequently found in works of fantasy fiction. These classes are given names, presumably because it gets awkward saying "I'm playing a person-who-uses-weapons-and-armour-really-competently!" all the time. For example, the fighter class can use armour and weapons well, and the wizard class uses magic and keeps spells in books. You'll have worked this out in a few minutes of reading the class descriptions.

However, being a member of a class doesn't mean your character identifies herself with the name of that class. A Fighter could be a Viking raider, a knight errant, a conquistador, or any of a thousand other possibilities. Similarly, there are loads of characters in fiction who cast spells and keep a library, and most of them aren't called "wizard." The Nomenclature Bugbear arises when we forget that class names are a convenience of game jargon and start thinking that they're recognised in-universe.

To be fair, this is an easy trap to fall into, as often the words used for class names do exist in-universe: They were taken from the fiction that inspires the game, and most campaign settings are also inspired by that same fiction. Most D&D settings do have people called wizards, and most of them are members of the wizard class, because the wizard class is pretty good at representing what wizards are in that setting. You just need to remember that in many such settings, in-universe nomenclature doesn't necessarily line up perfectly with the game terminology: In most settings, you can introduce yourself as a "thief" and people won't assume your character is a Rogue with the Thief archetype, because the only in-setting qualification to be a thief is to steal things, and any class can do that.

Getting back to your example...

You want to make a character who's a witch in the campaign universe, a person who uses subversive magic as an alternative to physical might and social prowess. You want this to be supported by the game mechanics and your GM. Those are reasonable goals. To achieve them, you need to do two things: (1) You want to find a class that fits with your concept, and (2) you want to work with your GM so that you have a shared understanding of what your witch is intended to be.

As your GM has pointed out, the warlock class isn't really what you're looking for. But your concept is still pretty broad, and that means it's flexible. With your GM's permission, you can simply pick any class that fits it, perhaps wizard, cleric, or - well, anything that uses magic - and have your character call herself a "witch" in conversation.

Once you've picked a class whose list of abilities sounds like your vision of a witch, explain your idea to your GM. It sounds like your GM doesn't object to your character's concept, so I expect he'll be receptive. As long as he agrees that there's no major dissonance between what your character can do and what she calls herself, you'll find that this solves your problem. It might take a bit of back-and-forth if he has existing nomenclature plans for magic-users in the setting, but eventually you'll have a character that you're happy with, and which your GM understands well. It's win-win!