Sure, it can be done that way. Back in the old days we never worried about processing (or even knew much about it, for that matter).
Processing the audio for shortwave will improve the efficiency and maybe readability of the transmitted signal, but isn't critical.
In more recent times, I used Winamp on the pc to playlist mp3s for broadcast. There are "add-ons" you can get that will process the audio for you in various ways, notably one called "Stereo Tool" that will compress the dynamic range (making the audio more level), cutoff some of the low freqs (say under 200hz) and high audio frequencies (above 12k hz anyways), which are unlikely to be received by standard shortwave receivers-- but still pass through the transmitter, wasting energy and making the transmitted signal wider than it needs to be.
One can do the same thing with programs like Audacity and WavePad, if you are creating a pre-recorded program from mp3 files, to use with an mp3 player or PC. Most of these programs mentioned have free options if you google them.
I've never used a hardware processor, so couldn't advise you on that.
Has this Valiant been re-capped to replace the old carboard-tube electrolytic capacitors, and yellow wax/paper capacitors?
THAT is important to do before you run it to any extent-- if the old ones are still in it, it can be dangerous.
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There are many audio mods on the net for the Valiant-- I'd advise using extreme caution before doing much of that. Widening the Valiant's audio by much has a nasty tendency to overdrive other parts of the transmitter and cause problems.
I owned two of these in the past. Loved the on-air results but they seemed more troublesome than some others.