Even if forget about the twin radio beacons onboard and ballistic measurements, and while it was ten times heavier than the first American ball,
by a strange coincidence it had size (58 cm), weight (85 kg), and shape close to the fission primer of then-mainstream RDS-4 bomb, which was sharing the warhead with then-mainstream R-5M IRBM.
And the next one, with Laika, had a pressurized compartment matching this ball size and position in the shroud, and with an additional equipment in the nose, making it look like a completed RDS-4-based (RDS-37) fusion warhead, with the dog chamber behind, where the control equipment is normally placed in reentry vehicle, making it weight ~500 kg in total.
As the satellites were being developed as a payload version of the R-7 ICBM, so big balls are not necessary bad.
Upd.
Corrected some textual ambiguity.
The fusionuke warhead of RDS-37 was using the fissionuke from RDS-4 as primer and RDS-6s's alarm clock as secondary.
R-5 used RDS-4's as is.