Client wants a draft

I contacted the owner of a small local business and offered to remake their old site.
They told me they were interested and asked to send them a quote.
I did, and they told me the price is ok, but first they want to see how the site will look like because "they don't know my professional skills" (even though I sent them a portfolio).
Do you think it's ok to just send them a screenshot of a WordPress theme edited with their logo and details?
I don't want to waste time actually building the site if I'm not 100% sure they'll accept.
Other clients always trusted me, this is the first time someone asked to see the site first.

I would just be straight forward with them, either tell them you dont work like that or maybe make them pay a fee for the draft... but yeah sounds like a skeptical client that might or might not pay you after you put in all the work into building that draft.

Only send them portfolios not look a like website, move away with super busy comments -already have projects in queue can't spend time on unconfirmed deals or
Tell them will start work after confirming the deal since it involves xxx hours of work

I have experience of proposing a wireframe first, which clarifies how to user will use the website and how it should be logically structured. Next is pixel perfect design done in e.g. Figma, consulted by client and then finally real coding / editing of Wordpress.

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EDIT:
anyway, there should be some forward invoice, only for the wireframe e.g.

Charge them a fee for the draft ($25 or something) which is deductable from the final price if they place the order

You need to be upfront with them and let them know what they are getting for the cost of your service. You shouldn’t be selling a custom design when you’re only going to use a premium theme. If somebody wants a custom design then set out the pricing up front whether you charge per hour or per project or per design. I start out by asking clients to send me website designs they like and ask why. For clients with a smaller budget I tell them I use a premium theme as the base and build their site on top of that theme. I still ask clients to send me links to other sites they like and ask why, but then I follow up their response to demos of premium themes and ask them to choose the one they like. In both scenarios the client has an idea of what their site could look like and with the premium theme they know what they are getting.

Never do work for free unless you’re getting something in return. As others above suggested I would change them for designs and your time if they aren’t willing to commit yet to your work. Tell them it’ll will be $X amount per design you send over and if they sign a deal with you then you can prorate the design cost off the build. The only issue you might have with this approach is sending the client designs and them backing out and never paying you.

I usually don’t work with clients until they commit and pay 50% upfront.