Designing shortwave radio receiver
Dual gate MOSFETs (tetrodes) have characteristics that make them very suitable for RF mixers. Typically RF is applied to G1 the first gate, and local oscillator is applied to G2. This maintains good isolation between oscillator and RF circuits, and low third order intermodulation (by which strong signals can wipe out nearby weak signals)

While just about any triode transistor (bipolar or FET) can be pressed into service as some sort of mixer, getting decent performance out of them is quite an art.

Better to build the circuit as designed if possible. Perhaps use a more readily available BF981 (more associated with VHF). perhaps two JFETs in a "cascode" configuration, which operates a bit like the tetrode MOSFET. (Figure1 on the Wiki : RF in to Vin, local oscillator to the grid (cough, gate) of the upper FET, though it is shown grounded in the article.

Or substitute a different mixer; such as a balanced mixer using schottky diodes.