the wax may just be on the surface without penetrating as the distance travelled meant the wax was setting as it goes
ice yes best idea but avoid heat until nothing else works
perhaps light wire brushing /scrubbing brush tooth brush /scourer what ever along the grain only
i wouldnt use paper towel initially as you want any wax "flicked off " by bristle or uneven face pulling along where as paper towel will tend to push into the uneven surface
remember iff you soften the wax enough to penetrate the wood you will never get any decent finish to go on evenly
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