Programmable edge platform for JavaScript header modification

Yes. Several edge/CDN platforms let you execute custom code in the request path and modify the URL and/or headers before forwarding upstream.

Platform	Custom edge code	Rewrite URL	Modify request headers	Notes
Cloudflare Workers	JavaScript/TypeScript, WASM	✅	✅	Very flexible; Worker runs before cache/origin and can construct a modified Request.Cloudflare Docs+1
Fastly Compute	Rust, JavaScript, Go	✅	✅	Designed specifically for programmable edge/CDN request processing.
Akamai EdgeWorkers	JavaScript	✅	✅	Runs JavaScript at Akamai edge locations; particularly suited to CDN/proxy transformations.
Vercel Routing Middleware	JavaScript/TypeScript	✅	✅	Runs before request processing; supports custom logic, rewrites and request-header modification.Vercel+1
AWS Lambda@Edge	Node.js/Python	✅	✅	Runs code at CloudFront edge locations, including viewer/origin request events.
AWS CloudFront Functions	JavaScript	✅	✅	Lighter-weight alternative to Lambda@Edge, intended for high-volume request/response transformations.
Netlify Edge Functions	TypeScript/JavaScript	✅	✅	Deno-based edge functions with access to the incoming Request/Response.
Fly.io	Machines/apps rather than CDN middleware	✅	✅	Can act as a globally distributed programmable reverse proxy, but the model is different from Workers/Fastly.

If your requirement is specifically

client
  ↓
edge function
  ├─ inspect URL
  ├─ inspect headers
  ├─ rewrite URL
  ├─ add/remove/modify headers
  ↓
origin

I'd narrow the field to Cloudflare Workers, Fastly Compute, Akamai EdgeWorkers, AWS CloudFront Functions/Lambda@Edge, and Vercel Routing Middleware.

Cloudflare is particularly direct for this use case: its documentation explicitly describes a Worker modifying the incoming request—for example, rewriting the URL or adding headers—before calling fetch() to continue through the cache/origin. Cloudflare Docs Cloudflare also has declarative Request Header Transform Rules if you don't actually need arbitrary code.Cloudflare Docs

Vercel's Routing Middleware similarly runs before the request is processed and supports rewrites and request modification; Vercel even documents adding/updating/deleting request headers in middleware.Vercel+1

If you tell me whether you're looking for (a) a CDN in front of an arbitrary origin, (b) an API gateway, or (c) hosting an application, I can compare the relevant platforms on latency, runtime limits, pricing, cold starts, header manipulation, and origin rewrites.