My understanding is that the Electromagnetic Pulse induced by a nuclear weapon is mainly due to the ionizing effect of the gamma rays released by the nuclear reaction. However, for this ionizing effect to produce a downward blast of electrons moving at relativistic speed to the ground (the cause of the voltage shock on the ground), the ionizing effect has to take place in a conducting medium.
The atmosphere is a poor conducting medium below 10km so any nuclear explosion below this altitude only provokes a mild shock. Little Boy detonated at about 580m above the ground and Fat Man at about 500m above the ground.
Beside altitude, the most significant factor determining the strength of the EMP is a the gamma rays yield, which is about 0,5% of the total energy yield of the detonation (according to Wiki). Little Boy had a total yield of of 16 kilotons of TNT. As you can see in the chart below, a 0,08 kiloton detonation yields a mild voltage shock even at high altitude.
Add to that the fact that electronics in 1945 was vacuum-tube based (transistors would only be developed in 1947) and one can safely assume that the effect of the EMP was negligible (especially compared to the direct thermal effect of the detonation).