Depends on how risk-averse you are. You can generally get an SLA that would allow you to have a hot-back up of that server, or you take the risk that it won't wail until you can afford the "better" solution.

Doing "high availability" coupled with "low budget" is ALWAYS going to involve some compromises.

If you keep your DNS TTL's low, the worst-case scenario is if the small server fails, you're doing exactly what you would have done anyways: making manual or automated DNS changes.

If the client is keen to keep costs down... and is amenable to it... then you could give him an alternative URL to use in the case of a catastrophic failure (i.e. your plane scenario).

Then it's up to you if you use two haproxies for active-active or just maintain two active-passive sites.