A hamster runs miles in a night and will not moderate the habit because the household is asleep, so a noisy wheel is a mechanical problem to solve, not a behavior problem to train away. Wheel noise usually comes from a short list of causes, and working through them in order usually finds the culprit before money is spent.
Work Through the Wheel Check Set First
Start with the wheel itself and check it by hand, out of the enclosure if that is easier. Confirm it spins freely, turning smoothly for several rotations from one push, without a wobble, a catch, or a grinding point in the turn. Confirm it is the right size, large enough that she runs with a level back rather than an arched one, because an undersized wheel both strains her and flexes noisily under her.
Confirm it is not rubbing the cage bars, since a wheel mounted a fraction too close will tap or scrape the bars with every rotation once bedding shifts it sideways. Then add a drop of suitable lubricant on the spindle if the design allows, using only a drop, wiped clean of any excess she could reach, because a dry spindle is the classic source of the rhythmic squeak that carries through a wall at night. Spin the wheel again after each single fix, so you learn which one actually silenced it.
Quiet the Room Around the Wheel
If the wheel itself now runs silently in your hand, listen to what the enclosure adds. Stand the cage on a mat so vibration stops traveling into the floor or a shared wall, move it away from the bedroom wall if it sits against one, and clear bedding she has packed around the wheel base, since bedding dragged into the mechanism rattles and slows the spin. A stand-mounted wheel that rocks in loose bedding will knock softly all night, so settle its base firmly before blaming the bearing.
Test the result at the hour it matters. A wheel that sounds acceptable in a busy kitchen at noon may still be plainly audible in a silent house at midnight, so one nighttime listen is the honest verdict on whether the fixes worked. Sound also travels through furniture. An enclosure on a hollow stand or against a thin partition wall turns small vibrations into a household noise, while a solid surface and a few inches of air gap can halve what the next room hears, so experiment with position before concluding the wheel itself is at fault.
When the Honest Answer Is a Replacement Wheel
If the noise survives the full check set, replace the wheel with a silent-spinner style wheel, a design built around a quiet bearing and a solid running surface, chosen as a type rather than by chasing any particular name. Size the replacement generously, so her back stays straight as she runs and her stride stays level, and keep the old wheel only until the new one is running, because a hamster without a wheel for several nights will redirect that energy into bar chewing and climbing.
Add the wheel to the weekly enclosure routine so the next squeak is caught while it is still small. KinsLe makes that routine easier to hold in a shared household, since Care Teams assigns regular enclosure tasks for each pet to family members or helpers and records each completed task with a timestamp, so the spindle check, the bedding clearance, and the bar clearance happen on schedule instead of when the noise finally wakes somebody up.