There is a few high watt amp that will retain the same good sound but with a master volume turned down.
My Vox AV60 can sound ok at low volume (AV30 and AV15 available)
Most 5/10 w have tinny little speakers that don't produce a lot of low frequencies but there is some gems out there I'm sure some RO members will have suggestions

What kind of music do you do ?
You're amp is too loud for who ? the neighbors ?

For recording and getting 'that sound' it's all about the speaker cabinet. Mic choice and placement are critical but if your cabinet isn't going to reproduce the sound you're looking for it's a dead horse scene. There are a ton of specialty low wattage purpose-built recording amps out there now. Most of them are "single-ended" tube designs and the circuit for this type of amp has been in use for 70 years or so. The biggest difference will be the type of power tube and the variety of tone controls as well as input sensitivity and output selections or what impedance's the amp will drive. So searching for one to work for you may take a bunch of research and possibly some trial and error or, if you have access to a store that carries this kind of thing, in-person auditions. The question will be, "what kind of sound are you looking for in a low-wattage amp?"

Since you have mentioned a Fender Hot Rod (assume it's a Hot Rod Deluxe) it would seem an amp capable of clean to filthy might be in order. Unfortunately this narrows the field a lot. Some are great at saturated distortion while not having a good clean sound, and others do clean really well up to that bluesy breakup only to collapse when driven hard.