How to approach other professors in a department when the potential advisor is unsure of his funding situation?
The simplest solution seems to be the best - just be honest with both. Everybody knows that funding can be very difficult, and no one would blame you for having more than one horse in the race. It is, in fact, expected of a good student to seek out options. But we can consider some options.

Logically there are four options. You discuss with both, you discuss with neither, you discuss only with your first priority (called A) or you discuss only with your second priority (called B).

Discuss with neither: Nothing good will come out of this - they cannot read minds, and don't know your intentions if you don't speak up.

Discuss only with A: If A's funding falls through, this risks becoming awkward with B. You don't, in fact, know if B for example has other plans if you don't discuss it.

Discuss only with B: If A's funding falls through and you get a place at B's team, this may be awkward as you still have to be in the same department as A.

Now ask yourself - are there any downsides from discussing with both? I cannot think of any.