Make Intimidation a Str based skill or allow player to choose Str\Cha, this is a very common rule used by DMs. It allows you to avoid illogical situations when tiny bard is more intimidating than brutal barbarian.
its even covered in the core rules - if it's logical and realistic to use a characteristic other than the default one with a skill, you can, but it's always a GM discretion.
Therefore, rather than it being a carte blanch option for the PC, it should be something that is available via specific dialogue options and be displayed as Intimidation (strength)