The first thing you need to nail down is exactly how many watts your LED strip draws, beacuse that determines the size of the power supply required, period. Trying to fit a tiny module before you know the power budget is just guessing. If the strip needs, say, 5 watts, you can use somthing much smaller than if it needs 20 watts. Always calculate the current draw (Amps) by dividing the total power by the voltage you plan to run the LEDs at.
For small decorative projects, you ussually want a small switched mode power supply (SMPS) designed for compact use, rather than a bulky transformer. Many manufacturers produce 'mini' industrial power supplies specifically for embedded applications. Look for units that advertise low-profile or DIN rail compatibility, even if you are just bolting it to the inside of a custom enclosure. They tend to be more efficient and smaller than general household power bricks.
If the strip is only pulling a few watts, you might find specific DC-DC step-down converters that take a wider input range, potentially even allowing you to run a tiny, enclosed power supply further away, but generaly, sticking to a dedicated AC-to-DC unit that matches your voltage (like 12V or 24V) is safer. Don't try to jury-rig a cheap wall adapter you alredy own; you need a unit with proper thermal management and documentation for the required input voltage.
Integration is also key. Even if a power module is physically tiny, it needs to dissipate heat. If you are tucking it into a sealed box, ensure there's enough airflow or adequate internal clearance so the module doesn't cook itself. Also, make sure your internal wiring is robust enough to handle the current safely. It's easy for those tiny connections to get weak and cause issues later on.