That has to be with just its fan running, not the compressor (49W at
10 EER would be only 490 BTU/hr, smaller than any room AC on the
market).

Try measuring it again, but turn the temperature setting way down to
force its compressor on. You may have to wait a few minutes
afterwards... most A/C's impose a time delay on compressor start after
losing power, to protect against damage from short-cycling.

Anyway, expect a power draw at least ten times as high when the
compressor's on, along with a brief, but very BIG current wpike when
it first kicks in.

I have a very small window unit rated at 5200 BTU/hr, which pulls
400-500W at 120VAC when it's compressor is on (40W for just the fan
and controls), but spikes to over 2500W(!) for a fraction of a second
on initial start. It's hard to catch that initial spike on a
Kill-a-Watt, unless it happens to sample at just the right time.

After starting this from a big inverter (Outback 3500W or Heart
Interface 2000W), my little Honda EU-1000i can keep it running, if the
power is switched over to it quickly enough with a DPDT transfer relay
and the compressor stays running rather than cycling.

Trying to get past that initial surge with just the Honda would
instantly shut it down.

> The 4.5" muffin fan I sometimes use with or w/o air cond. consumes
> 21 W.

Some 12V DC fans of similar size (120mm) pull only about 2W. They're
intended for computers, but can be mounted on stands for tabletop or
bedside use. A bit uly, but very practical...

A "high airflow" model might pull 4W, or less if you slow it down a
bit by reducing the voltage. Speed control is much easier with DC...
a multi-position slider switch and stack of diodes is one way.