For amateur pursuits this 'wobble' can be ignored as it takes many years and only causes ~0.05 ppm doppler shift.
It is important to note that the periods quoted in pulsar data (e.g. the ATNF Pulsar Catalogue) are 'barycentric'.
In the pursuit of detecting known pulsars, the observational data received will be 'topocentric'. In order to convert predictions expressed in barycentric form into the topocentric equivalent for the purpose of epoch folding at the correct period to reveal a pulse, other orbital effects must be taken into account. The annual orbit around the Sun of the Earth produces significant doppler shift on the pulse period of a pulsar, depending on the orientation the observed pulsar w.r.t to the axis of the Earth's orbit around the Sun. The magnitude of the diurnal doppler shift is dependent on the product of the cosine of the declination of the pulsar and the cosine of the latitude of the observatory. For Vela the annual doppler shift caused by the Earth's orbit around the Sun has a range of ~ ±48 ppm. The diurnal doppler shift for Vela for HawkRAO (latitude -34) is ~ ±1 ppm. There is a small monthly doppler caused by the Earth/Moon barycentre, but this only amounts to ~ ±0.02 ppm and can be ignored for amateur purposes.
Failure to take these doppler effects into account can prevent finding the correct folding period - hence a failure to detect a pulsar signal. Most amateurs (and professionals) use some version of TEMPO to calculate the current topocentric period of the observed pulsar for their individual observatories.