Oh - I see what you mean.
The first reset would come in as "Deep-Sleep Wake" and then the 2nd would come in as "External System".
I wouldn't need any extra delay.
That might work quite well.
The only reason for a reset would be either
1) Force a poll (they press once)
2) Reset (they press twice)
If they press the button while it's on (and polling), then they obviously wouldn't be trying to force a poll anyway.