That is not really an option and here is why. Both the Dolby and DTS streams are encrypted. You can't decode them without using their respective algorithms.
Neither Dolby nor DTS streams are encrypted. They use a non-trivial binary format, but there's no encryption or even obfuscation involved at all. You do indeed need to use their patented algorithms, and for commercial product, getting their license and passing their compliance tests is probably more than just a good idea. If you want to verify that there's no encryption, check e.g.
https://code.videolan.org/videolan/libdca
They[Trinnov] are licensed just like we are. What they get is basically the same, its code that they don't have access to.
I believe they have a license more akin to what Analog Devices or Texas Instruments have, i.e. they probably have the bitstream specification and sample source code from Dolby and DTS and use the full theoretical channel count and location, not just the limited and mostly fixed speaker configurations that AD or TI support in their code. AD and TI have put in the work to make the decoders run efficiently on "cheap" DSPs, at the cost of only allowing a limited set of parameters, and as a result, can be "easily" integrated in to new products.
It is a function of the Dolby and DTS modules that are embedded within the chip.
Not sure which DSP you're actually using, but in most cases, the code is stored on external flash and loaded into the internal RAM when the DSP boots, but I suppose since you get the DSP, the flash and the decoder libraries as a bundle, there's not much of a difference. But since you're posting here: Do you get the black box binary you use from Dolby or from the manufacturer of the DSP, and who provides support if it's not working as intended? Who is responsible for the code that decides if the bitstream currently received is PCM or a flavor of Dolby or DTS?
