any wood
can be used for tool handles, it's just some are better than others
You could make your shovel and mallet handles from willow, sycamore, oak, hawthorn, etc if you like. A sycamore shovel handle will not last very long if you leave it out, but it will still work alright. Willow might be worth a go, you don't see many broken cricket bats. Not tried it myself though I have to admit
I've got a pitch fork that has a 1 1/2" diameter hazel pole as a handle, it was a temporary measure half way through a day's work about 2 years ago. I know that when I come to use it one day the handle will snap off coz it's not the best wood around, but it took about 10 minutes to remove the old stump and fit the pole whereas an ash handle would've taken the time to go to the workshop and fit the handle (that would've been bought for £X or spent Xhours making the handle). So for me at least, the wrong wood is still more cost effective for that tool handle
Also, once you've made your first handle it won't take so long for you to do it next time. So if you decide that actually the willow/sycamore is really rubbish, you can still replace it with ash later without waisting wood on a dodgy first attempt