I'm no expert either ,but I just acquired a model 10 ,no dash ser # C544699.
It's no model 29-1
but again ,the mystery of the late 50s' ,early 60s' production continues.
Could C544xxx be one of the last mod 10s ? Heck ,in 1961-1962 Smith only made 147,000 M&Ps, yours ,and mine were just 2 more in the bunch.
I love it for what it is ,a sweet shooting old S&W 38 special.
Reegards ,,,,Al