Jurgen's charge isn't as suicidal in intent as it turned out to be. His cavalry unit had been successful over the two days of fighting to render the non-professional side of the army completely useless. Under the tradition of warfare prevalent in that era in our real world, he would have survived surrendering in both circumstances had he actually survived the charge.
If the 1st prince faction had succeeded then the noble heirs forming their cavalry would have had to be repatriated to their parents after surrender or simply ransomed back. The fact that they were noble heirs defending their households - which is exactly what they are traditionally and legally bound to do - effectively made them immune to execution. Plus the new separatist state would have had support from the Empire. If the 2nd Prince had executed the boys he would have triggered casus belli for the Empire to invade and lose his throne to whichever superpower won the fight for Baselland.
If the 1st prince faction had failed then the parents would have had to be punished, which may mean execution. That would mean the boys would have had to be kept alive because the NORTHERN NOBLES would rebel if they saw any hints of the abolition of nobility. These are the same nobles who came up with crazy tricks like registering Helmut as a boy to retain their fiefdoms, after all. The 2nd Prince would need time to reform his system and weaken the remaining nobles and he absolutely cannot afford to have the North rebel because that would automatically invite you-know-who to intervene. Furthermore, it's useful to have already-defeated underaged nobles as "allies" because he could then pass the management of their estates to professional regencies and have them stand as a counterbalance to the North. In effect, keeping the boys alive would have been the best option available to the 2nd Prince. He would have been able to take over their fiefs while keeping the facade of traditional noble succession, and he would have had the excuse to keep those nobles in check for their prior rebellion. This is something that commonly happened in our real history of Europe.
So either way the cavalry unit would have been safe (at least in theory) if they had surrendered given the traditional precedent. This is central Germany, not Imperial China. Jurgen's failure lay in his not understanding how fast his opponents adapted new ideas. Remember, last time Balzar himself called volley guns useless because that was the prevailing view in his military. Then a special trap had to be set to make them useful against a cavalry charge. Jurgen had no reason to think that they would have developed proper anti-cavalry tactics with those guns in the short time since the previous war just based on Balzar's report alone.
If the 1st prince faction had succeeded then the noble heirs forming their cavalry would have had to be repatriated to their parents after surrender or simply ransomed back. The fact that they were noble heirs defending their households - which is exactly what they are traditionally and legally bound to do - effectively made them immune to execution. Plus the new separatist state would have had support from the Empire. If the 2nd Prince had executed the boys he would have triggered casus belli for the Empire to invade and lose his throne to whichever superpower won the fight for Baselland.
If the 1st prince faction had failed then the parents would have had to be punished, which may mean execution. That would mean the boys would have had to be kept alive because the NORTHERN NOBLES would rebel if they saw any hints of the abolition of nobility. These are the same nobles who came up with crazy tricks like registering Helmut as a boy to retain their fiefdoms, after all. The 2nd Prince would need time to reform his system and weaken the remaining nobles and he absolutely cannot afford to have the North rebel because that would automatically invite you-know-who to intervene. Furthermore, it's useful to have already-defeated underaged nobles as "allies" because he could then pass the management of their estates to professional regencies and have them stand as a counterbalance to the North. In effect, keeping the boys alive would have been the best option available to the 2nd Prince. He would have been able to take over their fiefs while keeping the facade of traditional noble succession, and he would have had the excuse to keep those nobles in check for their prior rebellion. This is something that commonly happened in our real history of Europe.
So either way the cavalry unit would have been safe (at least in theory) if they had surrendered given the traditional precedent. This is central Germany, not Imperial China. Jurgen's failure lay in his not understanding how fast his opponents adapted new ideas. Remember, last time Balzar himself called volley guns useless because that was the prevailing view in his military. Then a special trap had to be set to make them useful against a cavalry charge. Jurgen had no reason to think that they would have developed proper anti-cavalry tactics with those guns in the short time since the previous war just based on Balzar's report alone.