Those are the only hand-sized examples I've ever seen of the "Dutch Hoe" or "scuffle hoe" or "oscillating hoe" or "stirrup Hoe".
A local greenhouse/market garden wholesale supply store had replacement blades for full-size scuffle hoes, but they were as expensive as a whole new hoe from Home Depot (but probably higher quality).
http://www.earthtoolsbcs.com/h...
Would you be able to replace the blade on your hand versions if you could find a replacement?
$6 replacement blade, screws close together:
http://clscatalog.com/index.ph...
(Wal-Mart also sells a replacement blade, but my IT dpeartment won;t let me go there to check:
https://bpb.opendns.com/a/www....
Here's a Lee Valley $13 hand "loop" weeder :
http://www.leevalley.com/US/ga...
Here's a classic scuffle hoe / hula-hoe with a 14" handle:
https://www.amazon.com/dp/B000DCOOEI/