Air Carrier departing MHTG continued take off after being advised by ATC to abort; noting their speed prohibited any abort maneuver.

Narrative

On push back; MHTG Ground Control informed us of a runway change from Runway 02 to Runway 20. We were unable due to runway limited take off weight and requested Runway 02 with 5 KTS tailwind. This required several transmissions back and forth with Ground Control while we requested a new flight plan and manually re-calculated take off data for a flaps 20 take off with 5 KTS tailwind. Then; while taxiing; Ground Control directed an immediate frequency change to Tower who cleared us for an immediate take off. Approaching V1; the Tower called for us to abort the take off. The pilot not flying replied 'Negative' as we would not have been able to stop on the remaining runway. When airborne; we got visual contact with a B737 apparently on approach to Runway 20. We passed well above the traffic with no TCAS alert. While re-calculating the take off data on the taxiway; we neglected to write down our clearance; so we confirmed it with Tower during climb out. The lesson here is not to rush or allow ATC to rush you and be especially alert at airports like this with a non radar environment.