A welder/gen set is going to use a lot of gas charging any small electronics, not to mention wear and tear on it.

You might be dollars ahead in the long run to buy a little Honda 1000 watt or so inverter generator. They are very handy, very quiet and very good on fuel.  I have one that seems to find a lot of uses, charging Milwaukee batteries and providing lights in a powerless out shed for one. Running freezers on a trailer is another. Nice clean power for computer or TV etc also.