I ran some numbers through a spurs calculator and it looks like you need a mixer with high IP4 to avoid spurs at the lower output frequencies, and high IP3 to avoid spurs at high output frequency. The output is limited to half the sine frequency unless the mixer has very good IP3.
2001MHz square wave
2000MHz sine wave
2 [1.0, 4000.0, 4001.0, 4002.0, 8002.0, 8005.0, 12004.0, 12005.0, 20010.0]
3 [1999.0, 2002.0, 6000.0, 6001.0, 6002.0, 6003.0, 6005.0, 10002.0, 10004.0, 14004.0, 14005.0, 18006.0, 18010.0, 22010.0, 30015.0]
4 [2.0, 3999.0, 4003.0, 4005.0, 8000.0, 8001.0, 8002.0, 8003.0, 8004.0, 12002.0, 16004.0, 16005.0, 16006.0, 16010.0, 20006.0, 24008.0, 24010.0, 28015.0, 32015.0, 40020.0]
2999MHz square wave
2000MHz sine wave
2 [999.0, 4000.0, 4999.0, 5998.0, 6997.0, 10997.0, 12995.0, 16995.0, 17994.0, 29990.0]
3 [1001.0, 3998.0, 4997.0, 6000.0, 6999.0, 7998.0, 8997.0, 10995.0, 12997.0, 15994.0, 18995.0, 19994.0, 26991.0, 27990.0, 31990.0, 44985.0]
4 [1998.0, 2997.0, 3001.0, 6997.0, 8000.0, 8995.0, 8999.0, 9998.0, 10997.0, 11996.0, 13994.0, 14997.0, 20995.0, 21994.0, 24991.0, 25990.0, 28991.0, 33990.0, 35988.0, 42985.0, 46985.0, 59980.0]
5 [2.0, 997.0, 4997.0, 5001.0, 6995.0, 9996.0, 10999.0, 11994.0, 11998.0, 12997.0, 13996.0, 16997.0, 22991.0, 22995.0, 23990.0, 23994.0, 30991.0, 33988.0, 35990.0, 37988.0, 40985.0, 48985.0, 57980.0, 61980.0]