No. There are an entire range of ways to generate an electromagnetic pulse using a non-nuclear pump. The simplest and most familiar couples a flux compression generator to a radiator -- a conventional explosive powered design. There are some alternative generator designs, but it quickly gets into classified space.
While not particularly complicated in theory, building these from scratch with reliable results requires a certain amount of precision engineering prowess. The Russians arguably did a lot of the pioneering work on these types of devices, and have sold such devices to a few different countries on the record, who knows who has gotten ahold of them off the record.
The limitation is their range. They can generate fields that have nuclear EMP strength, but the power quickly drops off after tens of meters meaning they have to be close to an unshielded target to have a good effect. Disruptive? Yes, but not at the level the scaremongers are suggesting. They are primarily useful against RF communications infrastructure, which is necessarily vulnerable.