As long as there is a filter in there should be ok. I may make one of those myself. I have an old kitchen exhaust fan that still works good laying on a shelf.
Actually making one out of steel isn't that much involved and you can clean it better than that wooden one on the other web site. If you aren't use to metal fabricating (or don't have the right tools), you can still make a wooden one, then line it with steel or aluminum for easy cleaning.
To do that just cut your wood to what ever size you want, then cut a piece of steel to cover each board (attach with flathead screws or small nails) prior to putting it all together. Then it's all lined and will be easy to clean with a solvent after you use it. You can still use the cheap plastic kitchen turntable. That should stand up to a few cleanings with solvent before it goes bad. They're cheap though so it's cheap enough to replace it ever so often. For a cheap and easy to work with steel or aluminum liner you can use light weight gutter flashing. Comes in rolls up to about 2 feet wide at the hardware stores or big box lumber yards.