My experience has been that modern depthsounders usually can't use the old transducers. However, it's worth a try if you can figure out make and model of what you have.
I have no experience of handheld depthsounders, but concur that, when you really want to know your
depth, you don't have spare hands or attention to look at an instrument you're holding in the water.
If your
hull is solid glass below the waterline, you can mount a new
transducer inside the
boat against the hull and get good results without putting a new hole in the boat. Find a spot away from the
keel and turbulence from the prop. Sometimes you can find a
transducer purpose built for inside mounting. If not, you can glass a short section of PVC pipe against the hull, fill with water or
antifreeze and mount the transducer there.