In 20+ years of working on my house, I've only had to replace glass twice at times when the sash had to be reinstalled quickly because of bad weather. In both cases, I primed & painted the sashes within 24 hours of applying the putty, which was still soft, but had formed a skin. And, in both cases, I completely forgot to check on the situation until months later, and found that the putty had hardened properly. In other words, I have no idea if the putty hardened in days, weeks, or months.
I just installed new glass in another sash, but this one could sit on the bench in the basement for a few days, if necessary. Should this be enough for hardening? If not, how long is usually about right?