My perspective here is similar to this question: Is it appropriate to include time to research if you don't know how to do something?, as both tackle the issues of who should pay for something that may only be relevant to a single project, but may also be legitimatly expected of a contractor.
In your field, are those tools standard? If I do 3D modeling for product prototype, I think it's acceptable for a client to assume I have one of a few industry standard CAD packages. If I work on the Microsoft stack, I think it's appropriate for a client to expect I use Visual Studio, or at least can interface seamlessly with developers that do.
Outside of this client, are those tools useful? Using the 3D modeling example, if a client expects me to have the same package they use internally - and there are (as I understand it, and let's just go with that for the example) a few CAD packages used industry wide - I think it's also appropriate to ask the client to cover a portion of the cost, somehow tied to how useful the package will be for other clients in the future.
Are those tools completely project specific? If this is the only project that the tools will be useful for (because they're for niche use cases, needed for legacy issues, etc) I think it's acceptable to expect the client to cover the cost, or provide the tools directly.
To your specific case, if the client seems to understand your concern about the cost it maybe worth asking why they want you to purchase the tooling, instead of providing it for you. It could be that they don't / can't license the tools easily for a contractor to use. Or it could be that they can't purchase software that is installed on systems they don't own (internal IT policy).
If for some reason it needs to be purchased by the contractor, and the tools are very project specific, I'd tell them there will be a $4000 setup fee (or similar) and that will go to the cost of purchasing and setting up the tooling. If they balk at that, you could offer to discount the first 4 months of hours (or however you're billing them), to offset some of that cost.