There is no such thing as a minimum power level at which a conductor will start radiating. If it radiates at all, then the radiation will be proportional to the power applied. Therefore, the maximum usable power in this circumstance is the power at which such radiation will interfere with (or damage) the receiver, and in order to know it you must test empirically or use electromagnetic simulation software.
However, there are two facts about radio design which you should consider before proceeding with the above principle.
First: You should not use brass strips. Not only that, you should not use wire either. In any RF system beyond the most basic, RF signals should be carried between modules or circuits through transmission lines, which prevent (or more precisely, greatly reduce) radiation away from the line. This prevents interference among the parts of your system.
(Within individual circuits, where transmission lines are neither possible nor relevant (since the point of the circuit is to do something other than carrying the signal unchanged), wiring between components should be short, to prevent radiation and other undesired effects. This is usually accomplished in modern radios using a printed circuit board and surface-mount components, but various techniques can be used depending on the desired operating frequency range.)
The most commonly known type of transmission line is coaxial cable, which is used to connect transceivers to antennas and also to route RF signals between boards/modules within them.
On printed circuit boards, carefully designed copper traces function as planar transmission lines (microstrip being a common design).
Besides preventing radiation, correctly designed transmission lines also support impedance matching, which is required to ensure radio signals are efficently transferred from the transmitter to the antenna; mismatches cause inefficiency and often cause destruction of the transmitter due to reflected high-power signals.
Second: Most transceivers do not transmit and receive on the same frequency at the same time. This is because it is extremely difficult to prevent the transmitted signal from being partly reflected back and overwhelming the receiver, even if you build everything correctly. Changes in the antenna due to weather, birds, etc. can disturb it enough to cause lots of reflected power.
Instead, a transceiver does one of the following:
- Transmits and receives at separate times, known as half-duplex operation. In traditional amateur radio this is accomplished with an obvious PTT button, but digital packet radio systems such as cell phones and WiFi switch back and forth many times per second.
- Transmits on a different frequency than it receives. In amateur radio this can be seen in repeater systems. This requires either using widely separated frequencies ("cross-band repeaters"), or using a and precisely adjusted "duplexer" which is a pair of filters adjusted precisely to the transmit and receive frequencies — and the transmitter and receiver must be well-designed with appropriate shielding and transmission lines so that the signal which goes through the air and bypasses the filter does not interfere.