There is so way to make this less painful for anyone. One, losing a child is incredibly painful for a parent. Second, you cannot predict nor control how people react to your actions. Just do it when you're ready.
There are ways to lessen the suferring.
imagine CTB in the date of your mothers birthday? Or CTB in chrhstmas time?
There are dates that could be strategicaly avoided.
As a personal example i was ready to CTB ths month, but then i realised my family is planning a big international 20 days trips abroad. I wouldn't be able to CTB and impact their nice vacation trip. So ill just wait a coulpe of weeks more, so they can enjoy their trip and come back. Ill CTB 1 week after their arrival.
Therefore picking the correct date/month is important and you can definetely lessen the suffering.