I'd say the HONDA 2.5hp should work fine, the 5hp will be more power than your "need", but the weight would be more of an issue in my mind. I use a 4HP Johnson (2-stroke) long-shaft (short-shaft will "work" but long-shaft is better). My Johnson 4 weighs 38# and does affect the trim of the boat, not much but the 61# of the Honda 5 (plus the fuel tank) will definitely affect the trim! I have used a 2 hp Johnson and a 2.3 hp Johnson, both were plenty of power for me (surprizingly, the 2 hp did better, I think the propeller pitch and gearing were better matched to the DS II than hte 2.3hp was) The 4hp I have gives me just that little extra power when needed, but usually I run no more than 1/2 -3/4 throttle.
On registering, what do you refer to by "1982 so no numbers"? If no one has used a motor on the boat before, or used her i na state requiring registration for all boats, powered or not (I though NH was one of those?) then I could see that there would not be any previous Registration numbers, but all boats built since November 1, 1972 have had a Hull ID number, so the only problem with lost paperwork is the lack of the title.
Can you contact the person that you bought the boat from? If so, have them send you a new copy of the bill of sale (or a re-written copy if they didn't smartly save a copy for their records). I believe that New Hampshire is a Title-required state, so that gets sticky....... HOWEVER, I assume that the paperwork that you lost included your title? I would contact the New Hampshire Boat Registration office and inquire about a replacement title, it will cost a small fee (Mass charges around $10 +/-), but hopefully they can do that for you, They may need the title number........and that would be a problem, but it is still worth a try. Once you have that title, you should be all set. At least in NH you don't have to worry about the mistake that I made when I bought my Widgeon, and then waited until 4 months later to register her. I didn't realize that I only had 20 days to pay the sales tax (I figured that I'd pay it when I registered.......oops!). Since NH has no sales tax....... you are safe on that!