Unfortunately, I don't think your PI's recommendation to use the acids sequentially will work very well. The two acids in aqua regia, or the peroxide and sulfuric acids in piranha, etc. either form a complex or perform separate roles in the reaction simultaneously that require them to be mixed.
There are other engineering controls that should be implemented for exothermic etching reactions beyond fume hoods and PPE. One is to perform the acid mixing and etching reactions from start to finish in an ice bath. Doing so will result in slower cleaning, but it will also result in slower undesirable side reactions -- like poisonous fume evolution and explosive boiling. Perform the reactions with freshly mixed solutions, and use only enough necessary to do the job. The heat generated during these etching reactions increases the rate, which further increases the heat, etc. Thus, catastrophic runaway reaction probabilities increase logarithmically with reactant mass under these circumstances, and small accidents are easier to deal with than big ones.
Finally, a specific note on HF. Treat it with the utmost respect. It can be deadly in small doses, will dissolve and deactivate your nerve endings before they've had a chance to register a pain signal with your brain, and will turn your bones to jelly. Debilitating health effects can set in for exposures as low as 12 ppm (4-hour exposure).
http://www.cdc.gov/niosh/ershdb/emergencyresponsecard_29750030.html If you must use it, I recommend taking a course on its safe use, and keep the calcium gluconate gel immediately available.