You are correct, Congress does control the purse strings, and has the final say on this. However, there are ways in which Trump can get around this.
Let's first look at what Trump actually announced:
Today, I’m instructing my administration to halt funding of the World
Health Organization while a review is conducted to assess the World
Health Organization’s role in severely mismanaging and covering up the
spread of the coronavirus.
Later in the press conference, he says with regard to the investigation that "We’re looking at a term of 60 to 90 days."
So this is not an absolute halt, but rather a temporary freeze. From here, Trump has two options.
His powers to halt the funds completely are subject to the Impoundment Control Act of 1974. The important bits of this law are sections 683 and 684, which describe the process by which the President can rescind or defer any congressionally appropriated funds. If Trump decides to completely stop all future payments to the WHO, he is required to send a special message to Congress requesting that the funds be rescinded. If this is not approved within 45 days, the funds must be used as originally planned. If, however, he merely decides to defer the use of the funds, he is only requires to send the special message; there is no process for Congress to challenge this, although payments may not be deferred past the end of the financial year.
If this avenue is not taken by Trump, he could make the argument that the 2020 fiscal appropriations act only specified funds under "Contributions to International Organizations" (pg. 286):
For necessary expenses, not otherwise provided for, to meet annual
obligations of membership in international multilateral organizations,
pursuant to treaties ratified pursuant to the advice and consent of
the Senate, conventions, or specific Acts of Congress,
So again, the Trump administration can make two arguments; firstly, that Congress didn't specify that the money was specifically for the WHO, but rather for any international multilateral organization, so funds can be removed from the WHO and spent elsewhere, and secondly, that payments to the WHO are not necessary to meet the "annual obligations" mentioned in the text of the act. This second argument would be fairly weak, as the WHO makes it clear that the assessed portion of the fees are a requirement of membership, however if Trump follows through with his more recent threat to leave the WHO, the fees would clearly not need to be paid.
To sum up, you are correct that Congress controls the power of the purse, but there are a number of pathways which Trump could use to either delay or completely stop payments to the WHO, either through the provisions of the Impoundment Control Act, or through creative interpretation of the language of the 2020 appropriation act.