I understand that the attenuator might not be adequate to reduce the power, but I'll test it and post back. I wonder if lowering the voltage and using an attenuator at the same time will have a better result.
I am not privy to a schematic. Mbarazeen claims that the circuits can handle a 3 volt drop. I certainly would expect the digital circuits, if their are any, to have a 5 or 3 volt regulator dedicated to them.
You won't damage anything. It is worth a try if you have an external power supply capable of supplying the current needed for all the circuits. I'm not sure if the power reduction will be linear...and I also fear that critical components will not be biased correctly. Even if they are, the most attenuation you can expect might be 50%...just a rough estimate. That would still be 2.5 watts. If the attenuator is rated for 1 watt continuous power, you will be exceeding it considerably. This will almost certainly damage it from heat. POWER is what occurs when one form of energy is changed to another in the form of WORK. The unit of measure for this is the WATT. Most transducers are not 100% efficient, meaning that the electrical energy that is being transformed into RF energy will experience LOSS in the form of heat. If 75% of the electrical power is converted to RF, then 25% has to be converted into heat. 25% of 1 watt is 250 milliwatts. 25% of 5 watts is 1.25 watts. Likewise, 25% of 2.5 watts is about 620 milliwatts. So, if you manage to reduce the amplifier output by half, and if the antenna and amplifier are 75% efficient, which isn't an unreasonable figure, you already have 620 milliwatts of power in the form of heat. That may not seem like much, but if the surface area of the dissipating components is small, that heat will be very concentrated.
The attenuator can probably handle more than a watt continuous. Perhaps a watt and a half. They often understate their abilities to prevent high failure rates. That still leaves you with a watt of power in excess. It won't last long before overheating and burning up.
The trouble here is, will this happen with you knowing it? Well, it will probably happen pretty quickly. Within 5 or 10 minutes. I suspect you'll be there observing through an FM radio. Be aware of a sudden, sharp decrease in signal strength. You will only have a few moments before the amplifier stage itself cooks with an open antenna circuit.
Then again, perhaps the website wasn't sure of the power abilities of this model. They did say (1 watt?) with a question mark.
I'm not going to tell you not to try this, I'm just offering justified warnings.
One thing you should do, is not drive the transmitter too hard with your audio input. I imagine it will be a CD player or computer? The audio output? Well, keep the volume fairly low. No need to blast it. Your carrier power will be unaffected by keeping the volume low, and this is the bulk of the continuous power. But your peak power output will be less if it isn't driven very hard. It might buy you a LITTLE wiggle room.
One other suggestion, and this is probably futile as well but here it is. If you heatsink the amplifier you might increase the power it is able to handle by a margin. Encasing it in a form fitted aluminum tube with fins, with silicon heat sink compound between the attenuator and casing might be a good start. A fan with good forced circulation would be another plus. And if you really felt bold, a copper coiled tube wound around the attenuator carrying refrigerated antifreeze would be an excellent heat exchanger. If you happened to have a water pump, a bucket, and dry ice, you could circulate the antifreeze through a second coil in a loop, passing the antifreeze through both coils and placing the second coil inside the bucket of dry ice. Effectively a radiator or heat exchanger. A lot of time, effort, expense, and labor. Better to get a proper attenuator....
And the dummy load is still out there as a possibility. I could build it for you, and will if need be, but this is a very easy project that you should be able to do on your own. I have faith.