I don't think it will work if the non-recommended wall wart is rated lower; and you will probably short out the component if it is too high.
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Are you sure it is millivolts and not milliamps? 800 millivolts is too low to operate most stuff.
Wall warts are rated for:
The amount of voltage they develop; this MUST be the same as the one that is replaced.
The maximum amount of current they can deliver; this must be equal to or greater than the original. Your device will try to draw a certain amount of current and the wall wart must be capable of delivering at least that much. If it can deliver more then that is probably better as it won't be working near it's capacity.
The connector must be the same. Some have the inside surface positive and some are negative. Get this reversed and smoke can develop.
If you are asking because you lost the original wall wart; they sell them at many different milliamps ratings at Radio Shack. For low power applications they have one that is switchable.
The connector is a separate item, so pick one with the right power, and then find a connector that matches. It just plugs in. The first one is no extra charge. They will charge you for more than one connector.
Sugar and Herman bring up very valid concerns. You can use a different wall wart so long as the voltage is the same and current capability are equal to or higher than originally specified. While voltage will remain consistent ( or relatively so ), the device will only pull as much current as it needs. Using a device with higher current capacity i.e. factory specified for 800 milli-amps and using a 1200 MA transformer is not a big deal. If you tried to use a smaller transformer that what you were supposed to, the device may work but could be glitchy and / or run much hotter than normal. You could also burn out the wall wart.
Before swapping wall warts though, i would verify if the wall wart is putting out AC or DC voltage. It should say right on the transformer itself and / or on the device itself. We typically take for granted that these little black boxes put out DC, but some "warts" and components are AC. As a case in point, all of the Musical Fidelity "X" series cans come stock with AC wall warts.
Once you're sure that you have the right type of power ( AC or DC ), the next step is to verify proper polarity. As Herman points out, one can have identical plugs but the connections are reversed internally. You can expect big smoke if you do something like that. Typically, the cost of the repair job is commensurate with the amount of smoke you saw come out. The more smoke, the higher the bill. Sometimes you get lucky though, but don't press your luck. : ) Sean