Can I use the EFHW-8010 model on the SSB part of band 3.7-4MHz with high power and tuner?

Yes but only with low power like 200W maximum. The SWR is high (over 3:1 ) and a reflection of 25% or more will dissipate on the transformer core which can lead to the destruction of the same. If you prefer a 3.8-4MHz sideband (SSB) operation, get an EFHW-7510-2K+ model which has low SWR on 75M and maintains the low SWR on other bands just like the EFHW-8010 model does.