I've never seen a pic nor heard of any 7th Army SSI with Airborne tab being worn by the 10th SFG.
The 10th wore the Airborne Command Patch upon activation at Fort Bragg, NC, on 11 June 1952 and continued to wear it after deployment to Europe in 1953 until it was replaced with the SF SSI which was approved in Aug 1955.
A number of the original 10th SFG Officers also wore their Infantry branch insignia with a number "10" superimposed atop the crossed rifles - but that was never authroized insignia.
The 10th SFG oval (dark green with red border) for the parachutist badge backing was authorized on 19 Sep 52 and was never changed.
The 10th SFG beret flash was approved with the authorization of the beret for SF in Oct 1961.
However, with Operation REFORGER, the 1-10th (which remained in Europe while the majority of the 10th SFG redeployed to CONUS) was authorized a separate dark green oval (without red border) and flash which contained three diagonal stripes of the German national colors (black, red, gold).
Richard