I don't know if that can actually be taken out. I feel like you'd need to replace the entire female jack in order to get what you want since the locking mechanism appears to be built into the frame. Did you have a specific cable in mind or something? Or did you just want a shorter cable? Because I'm using one on my HD558 that's pretty nice and not that expensive (by which I mean under $15). Downside is that cable ships from China so it takes a while.
What's your speaker setup look like? In terms of connections and all that. Cuz for example, my setup is computer to DAC by optical cable, then DAC to amp by RCA, then out to my headphones or banana plugs out of the amp to powered sub where speaker level out goes to the bookshelf speakers. Knowing what connections are needed is important to your choice since you aren't just thinking about headphones I assume. However, if you are only looking to get something just for the headphones and don't need to include the speakers and sub, then I do also here the Audioengine products
@Bansaku recommended are good ones. The Audioquest Dragonfly is also pretty good, which I believe has an MSRP of $150, but can be found on sale. Otherwise, I'm not sure what you could get in your budget. In case you're wondering, I'm using a cheapo (relatively speaking since audio equipment can get quite expensive) DAC/amp solution: Topping D20 DAC wtih Topping TP30mkII amp. At retail prices, you'd only be able to get the TP30mkII amp from my setup, which does also have a DAC taking USB input. I just like the D20 DAC better.
Even if your setup looks a little like mine, someone can probably recommend a suitable option with better performance and value than my setup. I just happened to get my setup super cheap (the D20 and TP30mkII cost me a total of like $80, which wouldn't be able to get either of them at today's retail prices). So considering this duo can send music to my ears through my headphones or speaker setup, I'm pretty happy with it, even though it's nowhere near best in performance; still does respectably in my opinion.