Many thanks for all the helpful responses. The joint between the beam and the base plate is essentially a lap joint as the base plate is wider than the beam and lies flat on top of it.
The fillet welds across the width of the beam are, of course, perpendicular to the direction of the stress created by the hydraulic cylinder pushing a log against the splitting wedge, which is parrallel to the web. the fillet welds between the underside of the base plate and the edge of the upper flange are parrallel to the stress and thus, as I understand it, more effective in securing the base plate. Not being an engineer, either, and a novice welder as well, I was not confident that the fillet welds would be sufficient to resist the shear stress of the baseplate against the beam, so I thought that additional shear resistance could be provided by a few plug welds.
It has been suggested, by a poster on another welding board, that I use a couple of 2"x6" slot welds for this purpose and that makes sense to me as it would another 24" of fusion parrellel to the web.