No, that's the neat thing about Costly Signalling. Giving the partner a month's worth of pay in cash is not equivalent, because in Costly Signalling the resource is wasted on purpose to demonstrate how inconsequential that resource is to the signaler. Giving the partner cash or giving to charity both have utility. A ring has no utility. Thus a ring is the only one of the three which can be a costly signal.
If you had a hundred billion dollars to your name, you wouldn't care an ounce about spending ten thousand on a diamond ring. Ten thousand dollars just doesn't matter. But a minimum wage worker cannot say the same. The ring is a socially established demonstration of this.
I am not sure I buy that reasoning. The ring certainly has utility from the perspective of the giver: the giver knows that it is going to elicit a positive response. A donation to charity cannot be worn, cannot be accessorized, cannot be shown off. I disagree with your assessment - in today's society, a ring has far more social value than a charitable donation.
The ring is shiny, and pretty, and can be socially displayed to elicit the attention of others.
The example you provide re-affirms my point. The evaluation criteria you are reverting to is wealth. And as a heuristic for wealth, the ability to purchase an expensive ring is a reasonable metric.
As a heuristic for a good partner, it is next to useless. As a screening criteria for the complex quality of "goodness" in partner, it is likely less than useless.
If you are evaluating partners purely on their wealth and willingness to waste that wealth to enter into a partnership with you, then a ring is a more reasonable criteria.
For an assessment on more nuanced basis (e.g. does the potential partner truly love me?), it is not a very good indicator, and may even be a contra-indicator precisely because it can be gamed easily.
Once again, I question the utility of screening based on this, even screening out on the basis of "not giving a diamond ring".