You're correct: there is no API to delete AWS Cloudwatch Metrics.
Just wait two weeks after your last metric has been pushed. It will disappear automatically.
Since November 1, 2016, CloudWatch has extended the retention of metrics (both custom and AWS NameSpace) from previous 14 days to 15 months.
But the CW console limits the search of metrics to 2 weeks after a metric is last ingested (which means if there is a metric in which no datapoints has been pushed for past 14 days then the CW console will not display it but you can still get it using the cli get-metric-statistics or by tweaking the console url to refer the correct resource name and start and end time older than 14 days).