Its a pity that a 10 gallon water heater costs more than a 50 gallon job.
You can find a 20 gallon mobile home one for 250$ or look at motor home water heaters, and get a small 120 volt element, maybe 1200 or 1500 watts, and you could plug it in under the sink without more wiring. That would likely be cheaper than a recirc system, and you can super insulate the unit too.
If you use a lot of water at that sink, your incoming cold could be the HOT in from the water heater. That should fill in the "lag" time