To save a model without touching pass false to save method:
$model = new Model;
$model->save(['touch' => false]);
Of course setTouchedRelations will work as well:
$model = new Model;
... // do what you need
$model->setTouchedRelations([]);
$model->save();
However you seem to want to use the current available values in the database, you could do something like this
$model->firstOrCreate(
[
'id' => 1
],
[
'updated' => DB::raw('updated_at'),
]
);
This basically selects the same previous value and inserts that value again.
I would personally go for the first option which is more readable and understandable ;)