GM,
I've never seen anyone use an SWR meter with an HT, but they obviously make small portable units for that purpose. I searched and didn't find too many models available, but I would recommend one thing ... If you think there's any chance that you may eventually purchase a mobile VHF/UHF rig, you may want to spend a few dollars more and try to get some instrumentation with better quality.
I checked the eBay units you listed and I'm not familiar with either, but at that price-point I believe the accuracy and quality will be questionable. If I had to choose between the two you listed, the Red Dot 1050A would be my initial choice. For your application, I wouldn't recommend a high-dollar Bird meter certainly, but I did find this
Comet CMX-400 that can be used on the VHF/UHF bands and is available in the UK, which may cut down on shipping costs for you. You'll have to inquire.
It does cost 79.95 GBP which converts to about $120.44 US. Might be worth saving a few extra dollars to buy this one. Now, you aren't going to be able to walk around with this meter attached, due to it's larger size, but for occasional SWR checks, it would work fine. It has 3 scales 30w, 60w, and 200w. It will also show forward and reflected power and PEP*. Min power for this meter is 6-watts, so it may not be sufficient to work with your handheld, since most are 5 watts max.
The purpose for using a meter of this type is to measure your antenna's efficiency. An ideal transmission line would have an SWR of 1:1, with all the power reaching the destination and no reflected power. An infinite SWR represents complete reflection, with all the power reflected back down the cable. This can damage your transmitter. When experimenting with new antennas, always check at low power settings initially, in case the SWR is high. You can tune the antenna from there. The inline coax adapter should not alter SWR readings to any substantial degree.
I'm sure some of the other fine members here will chime in. I hope this helped you a bit.
* Peak Envelope Power (PEP) - means the average power supplied to the antenna transmission line by a transmitter during one radio frequency cycle at the crest of the modulation envelope taken under normal operating conditions.