I'm assuming you want to save the Voices and other settings without saving any Style settings, so you don't need to make any changes to the Style settings-- just set up the Voices, Reverb, Chorus, etc. the way you want them. Then press the SONG button, but don't worry about choosing a Song-- just hold down the MEMORY button and press whichever REGIST MEMORY button (1, 2, 3, or 4) that you want to save the settings to.
Edit: Press the SONG button only if it isn't already lit up-- i.e., you want to save the Registration while the SONG button is lit.
After that you can change the Voices, the Style, etc. and start playing. When you get to the point where you want to switch to the Voices you saved, press the appropriate REGIST MEMORY button to recall that Registration and the Voices will change as desired but the Style will stay the same. I tried it and it works.
Here's a step-by-step example for you to try. Let's suppose I want to start with a modified Piano sound layered with a Strings sound, then switch to a Trumpet sound by itself, then switch to a Synth sound by itself, then switch to a Guitar sound layered with an Organ sound-- and switch back and forth between any of those while I'm playing.
I'm going to start by pressing the PORTABLE GRAND button, just to quickly set everything to the default "power on" settings. I'll use Voice 001 (GrandPno), but to make things interesting I'll change its parameters so it sounds more like an electric piano. Pressing PORTABLE GRAND selects Voice 001 automatically, but I could also select Voice 001 manually. Anyway, once I've selected Voice 001 (or pressed PORTABLE GRAND) I press the FUNCTION button, which takes me to whichever Function was last selected-- which should be StyleVol if I've justed powered up the PSR-E443. I then use the two CATEGORY buttons (+ and -) to go forward or backward as needed until I reach the Main Voice parameters. I'm going to leave M.Volume at 122 (the default for Voice 001), the M.Octave at 0 (default), the M.Pan at 064 (default), and the M.Reverb at 012 (default). However, I'll change the M.Chorus to 127, the M.Releas to 096, and the M.Reso. to 127. This should make the 001:GrandPno Voice sound more like a cross between an Electric Piano and a Synth. Next, I'll press the DUAL button to turn on the Dual Voice. Then I'll set D.Voice to 069:Strings, and increase the D.Volume to 070. Now I'm ready to save. Since I'm still in the Function menu, the SONG button should already be lit up, so I don't need to press it-- I can just save the settings to a Registration. So I hold down the MEMORY button and press the REGIST MEMORY 1 button.
Edit: Correction-- When you press the FUNCTION button the PATTERN, SONG, or STYLE button will light up depending on which one had been pressed last. For example, if you press PATTERN and select a Pattern, then press VOICE to select a Voice, then press FUNCTION, the PATTERN button will light up. So go ahead and press SONG before you save the Registration, to ensure that SONG is lit up.
Now I'm ready to set up the second Registration, a Trumpet sound by itself. I'll press the PORTABLE GRAND button again, just to reset everything. I don't want the Trumpet to have a vibrato, so I'll select Voice 506:Trumpet1. I don't want to modify its basic sound, but I do want to increase its volume, so I press FUNCTION and go to M.Volume, which I increase to 122. Now I'm ready to save. Again, if I'm still in the Function menu then SONG should already be lit up, hence I don't need to press it. (However, if you didn't use the PORTABLE GRAND button to reset everything then the Dual Voice may still be turned on, in which case you'll need to press DUAL to turn it off.) I hold down MEMORY and press the REGIST MEMORY 2 button.
Now for the third Registration, a Synth sound by itself. I press PORTABLE GRAND to reset everything. I'll select Voice 158:Fargo, then press FUNCTION so I can modify it a bit. I'll increase M.Volume to 122, then set M.Reverb to 000, increase M.Chorus to 127, decrease M.Cutoff to 032, and increase M.Reso. to 127. Then I'll hold down MEMORY and press REGIST MEMORY 3. (Again, there's no need to press SONG if it's already lit up.)
And lastly, I want the fourth Registration to be a Guitar layered with an Organ. I press PORTABLE GRAND to reset everything, then select Voice 045:60sClean. Next, I press FUNCTION and increase the M.Volume to 122. I'll increase the M.Reverb to 056, decrease M.Chorus to 000, decrease M.Attack to 000, decrease M.Releas to 032, increase M.Cutoff to 080, and decrease M.Reso. to 000. Then I'll press DUAL to turn on the Dual Voice and set D.Voice to 030:Full Org. I'll increase D.Volume to 075, set D.Octave to 0, increase M.Cutoff to 075, and increase M.Reso. to 100. Then I'll hold down MEMORY and press REGIST MEMORY 4.
Now to test everything. I'll press PORTABLE GRAND again, just to reset. I'll press the STYLE button, press ACMP ON/OFF to turn on the Auto Accompaniment, and press START/STOP to get the Style going. I'll pick Style 009:8Beat and start playing. Since I'd reset the keyboard it should be playing with Voice 001:GrandPno. Now I can start pressing the REGIST MEMORY 1, 2, 3, and 4 buttons while I'm playing without it affecting the Style. Just to be sure, I'll change the Style to 010:Off Beat and press the REGIST MEMORY 1, 2, 3, and 4 buttons again. The Voices should change but the Style should stay the same.
On the other hand, if you do want to save the selected Style, all you have to do is make sure the STYLE button is lit up when you save the settings to a Registration.