Yes it's back to 1967 again with The Year Of The Puppet.
The Icelandic version of Puppet On A String was recorded by Helena Eyjólfsdóttir and is titled Þú kyssir mig.
In the alternate universe where Iceland entered Eurovision in the 60's, Helena is the dream songstress to have brought the trophy to Reykjavik. Her early work includes coverversions of jazz standards as well as international pop classics.
Not uncommon in Iceland, Helena released her first record when she was 11 years old. Most of her work was recorded in her teens. She sang in several groups and with jazzbands like the Atlantic quartett, Gunnar Ormslev, Björn R. Einarsson and Svavar Gests.
She still performs occasionally but is withdrawing slowly from the music business.
Þú kyssir mig is available on CD 'Hvítu Mávar', a compilation of Eyjólfsdóttirs early work which also includes her version of Boom bang a bang (Og þú).
She also recorded an Icelandic version of Beg, steal or borrow probably with a band or duo. (Details and recording wanted)