Interesting to know you can get it running without DOSBox in Win7, something I'll be looking into when I upgrade to Win7! Are you running the Win95 version?
I can point you to my thread about how I got it to work perfectly on XP (at least for me, on SP3 currently): How to get Need For Speed Special Edition working perfectly in Windows XP
Not sure if that will work on Win7 though. Try disabling the sound first, if it runs smoothly then it's something to do with that...
My PC spec: Win10 64bit, i7-4970K (not overclocked), KFA2 GeForce RTX 2070 SUPER, Creative Soundblaster ZXr, 16GB RAM, Asus Z97-A motherboard, NZXT 410 case, ROG Swift GSYNC monitor