I will just use Node Cluster. Using cluster, a master can create a multiple workers, which means your cron wont block incoming request. Just make sure that only 1 worker doing the Cron. 
I have never working with node-cron before, but I have experience with the SyncedCron. But should be the same.
For the http client there are a lot libraries doing this, you can check Request or httpclient.
Your code should look something like this :
var cluster = require('cluster');
var http = require('http');
var numWorkers = require('os').cpus().length-1; // just give 1 cpu for OS to use, or maybe 2
if (cluster.isMaster) {
   console.log('Master cluster setting up ' + numWorkers + ' workers...');
   var cronPID=null; 
   for(var i = 0; i < numWorkers; i++) {
     var worker=cluster.fork();
     if(i==0){
      //instructing the first worker to assume role of SyncedCron.
      worker.send('you do it!');
      cronPID=worker.process.pid;
      console.log("worker "+cronPID+" choosed as Cron worker!");
     }
   }
   cluster.on('online', function(worker) {
       console.log('Worker ' + worker.process.pid + ' is online');
   });
   cluster.on('exit', function(worker, code, signal) {
       // have to revive the worker
       console.log('Worker ' + worker.process.pid + ' died with code: ' + code + ', and signal: ' + signal);
       console.log('Starting a new worker');
       var newWorker=cluster.fork();
       if(cronPID==worker.process.pid)
       {   // need to re-elect a new cron worker! 
           newWorker.send('you do it!');
           cronPID=newWorker.process.pid;
           console.log("worker "+cronPID+" choosed as Cron worker!"); 
       }  
   });
}else
{  // worker sides
   process.on('message', (msg) => {
      // validate your message that you get
      // if validated, create a cron job here
   });
   // create your express below, I assume you use express instead of node's http library
   var express = require('express');
   var app = express();
   app.post...........
} 
Note :  
- To revive the master, use something like "forever"
- Your server should have multiple core, at least 4 but I recommend more (8 maybe?).