How to Tx CDMA signal physically using an existing point-to-point modem?
If underwater communications is as complicated as I expect it to be, you get reflections from your own vessel, the ground, larger swarms of fish, and doppler due to water currents, and interesting pressure-dependent nonlinearties. An interesting field, indeed!
Now, that puts your modem in the position to have to compensate a lot of interesting¹ effects:

High attenuation
Doppler due to currents
Reflection on you vessel, ground, fish, submarines, cables, density strata, and hence a multipath channel
Frequency drift
potentially strong nonlinearity due to transducers and density effects in greater depths
…
Temporal variation of all the above effects

Thus, your modem will have to not only add error correction to the data bits you give to it, map these bits to some sort of symbol, and modulate that, and reverse that at the receiver. It will also have to estimate the channel and revert it; that's what frequency, phase and timing synchronization are all about, and what equalization does to revert a multipath channel as far as possible.
But the channel estimation would fall flat the moment multiple modems are transmitting.
Hence, you can't just add CDMA as extra layer to this problem that you can address on the data-providing side of the modem. You need to redesign the modem to be able to work as CDMA modem.

How to Tx CDMA signal physically using an existing point-to-point modem?

Redesign the modem.
Since you say in the comments that you've worked with SDRs: exactly like that, you'd develop your whole system in SDR software, simulate it, evaluate performance and improve it before you start working with &quot;real&quot; hardware transducers. One of such might be your current modem, but with a pretty different firmware that would be a port of your prototype to the specific Blackfin platform.
Maybe this talk (slides, paper) is a nice starting point for you; they do long reach, low speed communications using SDR approaches.
 
¹ and "interesting" here is the engineering definition of the word: "your rocket explodes whenever someone installs a printer in the office building? *Interesting!*"