I've done it, it wasn't elegant, but it can be done given the following restriction. The control housing must be reversible, i.e., designed for use as a side control to be mounted and hooked-up for use on EITHER side of the hull - port or starboard.
Given your old layout, you had a right-side (starboard) configured control, where the handle sticks out to the left. To effectively use it on a center console, whereas we are used to running boats with controls to the right of the helm, you would mount it to the right-hand side of your new center console, but it must be wired or connected as a left-hand mounted side control unit, where the handle now sticks out to the right.
For most controls that I am aware of, mainly OMC but some Yumster experience, this simply means that the control hand mounts on the "other" side of the control. I have an old MErc side control, but haven't looked into it, to see if it could be revered. Cables are still routed the way they were for the most part, but you may need to 'flip them' if one needs to be the inner-mounted cable trunion and the other cable on the outer-mounted cable trunion, for where they connect to and are activated by the control handle.
Be aware not all side controls were designed for either left or right hand/reversible use!
If you look at the 1st tin I modified (in my signature) I converted that hull from a side console boat to be a real center console. I got lucky and the side-control was reversible. Unfortunately you cannot see this detail in the picture. But as I say, it isn't elegant, as it tends to mount the control down and off the rear side (at the corner) of the console. Where it gets really UNelegant is in the cabling, as they need to stick out in the open somewhat before they take the bend to route back in and under the console main helm, to wherever or however that they then run back to the stern/OB.
If I were you, I'd try to find a used binnacle control mount. You can also make or get faceplates to put the ignition, choke/prime, warning horn and/or ignition kill circuit hookup mounted to other places on the helm, like on the vertical bulkhead. They do not need to be run out of the control mount itself.