In High school DxD, Issei "sacrifices" his arm to get the balance breaker form. But what does sacrifice mean here? He still has his arm and he can still control it.
Basically what happens is that as you said, Issei gives his arm to the dragon in return he get balance breaker. the arm that he traded is now belowing to the dragon, no longer a demon, that is why he was able to hold the cross or the holy water without being hurt in the fight between him and the phoenix.afterwards, the dragon power starts to take over his arms which stops him from having his normal arm and akeno had to suck out the dragon energy for issei could do whatever and not expose that he is a demon.
long story short, he has control over his arm but if akeno wasn't there, his arm would literally be the arm of the dragon Hope this helps