How could it lead to disbelief...all he would have to do, is talk to them.
How do you know your soul would be lost? Doesn't suicide mean you lose your soul?
Well for one thing, is this particular case he would never have had the opprotunity to speak to his people and explain his position. The Catholic church was persecuted by the most barbaric of means during Henry VIII and even worse during Elizabeth. He certainly knew this would be the result.
John Fisher refused to aknowledge a falsehood as true, he did the right thing. The fact that he lost his life because of it was not his choice, but the choice of those who chose to take it. He refused to lie and it cost him his life, this is not suicide since death was not his desired result.