There is not thirty six different solutions. The proper way to die for a noble is either comfortably in his bed but even better on the battlefield. A death in combat is a very noble way to die. If this death was common for many nobles under the reigns of Louis XIV and Louis XV ( especially during the Seven Years War ) it of course did not concern everyone.

The only proper way to execute a noble is beheading. Hanging, quartering and other awful supplices are not for the nobility, they are for low people, peasants, regicides, ...Etc There are not many other methods that would be seen as acceptable simply because it was a privilege of the nobility as an order to die, in case of execution, by beheading. So technically it was not a choice for the king since it was one of the rights that had to be respected. Plus, an other privilege of the nobility that in case of a trial it was made by other nobles. Most of the time a parliament but in case of a very difficult trial it could go al the way up to the conseil du roi ( King's council ). Even Louis XIV could not just snap his fingers and have everything he wanted. Even if it helped to be him.

Nobles were not exempt of the question ( name given to torture ) however. The Marquise de Brinvilliers was executed by beheading in 1676. Only her condition as a marquise stopped her from being burnt at the stake like other poisoners and witches who were her accomplices.

This is why the guillotine was quite a big deal even during Louis XVI's reign and later during and after the Revolution. The notion that everyone was equal in front of death was difficult to understand and accept for many. Some deaths were judged better than others.