Dry mix mortar?

[Smileysmile1]

Hi,
I'm not sure if this correct group but here goes.
My house was built in 2001.
It has steps leading to front door.
Metal railings either side secured to a stepped wall. Over the first years the steps moved then settled.
Which means the mortar between the concrete slab steps and wall aren't flush anymore. The steps have moved down an inch.
I chiselled the old mortar away leaving one inch gap between step and wall. About 2 inches deep.
Some gaps are smaller.
Would a dry mixed mortar be the best way to go to fill gaps? Thanks

 

[23vc]

I’d make sure they’re not going to move any more first

 

[Smileysmile1]

No.This bellway house was built in 2001.
Any movement was years ago. It's been a job on my list.
I've attached photos of the gaps left after chiselling away the old grouting.