There's an adjustable EQ filter in the Zoom B1 Four that can be set to act either as a LPF, HPF, LoShlv or HiShelv filter with an adjustable slope from -1dB/Oct to -12dB/Oct, the latter pretty much being the standard for LPF's and HPF's, thats about as cheap as it comes, and I would dare claim for something as relatively simple as a HPF the quality should be as good as any digital HPF on the market, and even though it is a multi effect it is still slightly smaller than about 2 Boss sized pedals pressed agains each other side by side.
Another slightly more expensive option, but still relatively cheap compared to most other HPF available on the market, is the optional HPF, fixed at 40Hz, build into the ART Tube MP Project Series tube preamp, though it would require of you to run it through the preamp, it utilizes a starved tube plate though, I think I read somewhere around 70V, where the tubes are designed to run at much higher, around 200V to 300V plate voltage, but I use it myself as the preamp in my "ampless" setup and think it sounds lovely.
Contrary to common believes the starved plate voltage actually makes the tube color the tone more than what is the case at higher plate voltage, though the character of the tube does change some at lower voltage, also be aware that the cheap Chinese stock tube sounds pretty crappy, so if you go this route I would advice swapping it out for one of proper quality, personally I use the EHX 12AX7-EH preamp tube for my Art tube preamp.
As said I love what it does for my tone, and I do in fact have the build in 40Hz HPF activated too, which seems absolutely perfect to me, tightens up the low end and makes the tone clearer.
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