Yes, if the creature you control has deathtouch, it will apply to Fall of the Hammer
The rule on deathtouch is 702.2 in the comprehensive rules. The one that matters for this question is rule 702.2b:
702.2b A creature with toughness greater than 0 that’s been dealt damage by a source with deathtouch since the last time state-based actions were checked is destroyed as a state-based action. See rule 704.
And the referenced rule from 704 is pretty much a restating of this same rule:
704.5h If a creature has toughness greater than 0, and it’s been dealt damage by a source with deathtouch since the last time state-based actions were checked, that creature is destroyed. Regeneration can replace this event.
These rule mean if the source of damage has deathtouch, then any damage is enough to destroy the creature. So the real question here is what the source of damage is, and the source of damage is explained at the beginning of Fall of the Hammer"
"Target creature you control deals damage equal to its power to another target creature."
Fall of the hammer specifies that the damage is being dealt by "Target creature you control", since the creature is the source of the damage, abilities like Deathtouch and Lifelink will apply.
Note: As an example of a similar card where the creature abilities wouldn't apply, take a look at Dragon's Breath. The card lets you choose or reveal a dragon as you cast it, and uses that dragon's power to set the amount of damage, but it still specifies that the spell, not the creature, is the source of the damage:
As an additional cost to cast this spell, you may reveal a Dragon card from your hand or choose a Dragon you control.
Dragon's Fire deals 3 damage to target creature or planeswalker. If you revealed a Dragon card or chose a Dragon as you cast this spell, Dragon's Fire deals damage equal to the power of that card or creature instead.
Fall of the Hammer
is the source. I thought it would apply, but wanted confirmation.