HHG can occur with very little pulse energies at 800. It was shown with microJoules of laser energy in a gas filled capillary in 1999 [C. Durfee, et al., PRL 83, 2187 (1999)]. That power can can generate relativistic harmonics with solids as well [J. Easter, et al., Opt. Lett. 35, 3186 (2010)]. Practically every paper you can look up for phase matched gas harmonics operates with 800 nm and energies on this order or lower.
You didn't mention pulse duration of your laser system, but 2-4 mJ should be enough for coupling into a hollow-core capillary; combined with a chirped-mirror compressor, you could generate few-cycle pulses with hundreds of microjoules of pulse energy. This could give you more freedom in terms of what kind of high harmonics you can generate.
That femtopulse and energy should do ---- you can find some interesting experimental setups in our publication list. Although experimental detection of SHG and THG could be challenging so it will take time and would be best if you have someone with experience to help you out.