With the current design of the original Resident Evil's map, I don't think it would work with the Resident Evil 4 engine at all.
Resident Evil was all about surviving. Killing when you had to, but avoiding if you could. Your character movement wasn't fantastic, your guns were slow and clunky and you were mainly exploring small, confined, claustrophobic areas with only a handful of threatening enemies.
Resident Evil 4, however, laid the survival aspect to rest. You could kill every enemy in the game and not worry about having a shortage of bullets to defeat a boss. The controls were smooth and worked, the guns were fast, upgradable and very easy to use in all situations and the areas you fought in were often large, open spaces with plenty of room to run away and almost plan your combat as it comes with a fair amount of ease.
I just don't think the two could cross over that well. There was a reason RE4 had different enemies. You had intelligent beings with weapons who could run and attacked in huge groups, yet it was counterbalanced by the much improved combat and weapon system. A group of Ganados in the first RE would have been near impossible to kill, but 4 gives you the power and the right kind of game to be able to beat them.
Now, in a game set in pretty much just a mansion, a garden and a lab, with slow enemies that are small in number, the over the shoulder view and the laser pointer on the guns allowing you to shoot a zombie in the knee and then suplex him onto his head would just take away all of the threat they once had. Then of course, with the size of the map, the game would be possible to complete in under an hour.
If they did remake it with the fourth game's engine, they'd have to drastically expand the map. Maybe giving you the chance to explore outside of the mansion and its surrounding area or something. Though I genuinely don't think it's possible to expand the map of the first game enough to actually make it anywhere near the size of the fourth.
Then, the enemies would have to be a lot harder. Every zombie would pretty much have to be a crimson head and there'd have to be a far, far greater number of them. Same would go for Hunters, dogs etc.
All in all, it'd be very hard to pull off. The only game I could see even slightly working with the RE4 engine is Nemesis, as it has the largest map, which would be a lot easier to expand (you have the whole of Raccoon City to play with) and the areas could be a lot more open and there are far more enemies around. It was generally the most action based out of the "classic" style Resident Evils.