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When people use the word 'quant' within the realm of trading, they might refer to two different things. People who do tons of coding, as you alluded to, to develop models. The other, just 'quanty' products.
For example, a CDO trader will be considered more quant than an equity trader. As a CDO trader you aren't making CDOs or some elaborate pricing model to figure out what you should trade the product as (proprietary models are given to you, developed by 'quants'), but rather you are simply trading a product that has more a more developed mathematical backstory. For this reason, CDO trading desks will prefer someone with a more technical background as they will seemingly be able to pick up on the product quicker, understand the details within the pricing scheme and translate this understanding of a more complex, mathematical product into relevant knowledge; given that x will happen to rates, what will happen to each of the components that influence this CDO and how can I use this info to trade the product. This of course needs a person with very good math skills and the ability to understand complex workings, not necessarily, but many times coincidentally, people from STEM backgrounds.
So when you mean pigeonhole as a quant, I'd imagine you mean positions entailing heavy programming? If you want a market-relevant role that utilizes more math abilities, then lean towards the structured products arena. If you don't mind about the market nor the programming, going into a traditional quant role can be great in regards to lifestyle, pay, hours, security (if you're good, the firm will make sure you stay on). If you want a happy middle, (interest rate,fx,etc) structuring would be a great position as well. Good hours (on an IR desk, traders got in around 6, structuring around 8-9..), cerebral, project oriented work, and yet still more interactive than typical quant jobs as you will be doing structuring for clients and therefore will be spending much time on back and forth, updating ideas due to medium-long term market expectations, etc.
For algorithmic/quant trading, you don't need programming skills to succeed. A lot of it is algorithm/strategy design, and the coding is left to the quants/developers (though if you can code, it helps a lot to bridge the communication gap). For more quantitative strategies, a solid understanding of math/stats is more important, and for HFT MM, it's even less complex (literally you just want to buy low and sell high).
It's similar to what they do at Google/Microsoft/etc. They have "program managers" (PM) who do more of the design whereas the developers actually code. It's a little different though because they're tech companies. The PMs also need to be able to code to some extent, but even then that is not their main role.
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To be honest, if you really want to be able to use your quant skills creatively you want to go to a hedge fund that is focused on more complex products (ie a volarb fund, a correlation fund, structured credit etc). At these types of places the job is to basically be creative and try to come up with trade ideas/strategies, and what is good about it is that maths become a tool, and you use it however you want to do the analysis on your ideas.
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